Handle Page refresh on DropDownList change inside GridView using UpdatePanel in ASP.Net

I have checked your. There is no page postback happen.

There might be others causing the issue. You need to check that.

Refer the code that i implemented with datatable as per your provided html and code.

HTML

        <form runat="server" role="form" class="form-horizontal">
        <asp:ScriptManager ID="scrManager" runat="server"></asp:ScriptManager>
        <asp:UpdatePanel ID="upPnl" runat="server" ChildrenAsTriggers="true">
            <ContentTemplate>
                <div class="well" style="width:90%">
                    <div class="form-group">
                        <label class="control-label col-md-2">Department <span style="color: red">*</span></label>
                        <div class="col-md-4">
                            <asp:DropDownList ID="CmbDepartment" CssClass="form-control" runat="server" AutoPostBack="true"
                                OnSelectedIndexChanged="CmbDepartment_SelectedIndexChanged">
                            </asp:DropDownList>
                        </div>
                    </div>
                </div>
                <div class="row">
                    <div class="col-md-12">
                        <div class="table-responsive">
                            <asp:GridView ID="GridView1" runat="server" Font-Size="Small" AutoGenerateColumns="False"
                                CssClass="table table-striped table-bordered table-hover table-responsive table-colored table-info"
                                EmptyDataText="No records has been added." OnRowDataBound="GridView1_RowDataBound" Width="90%">
                                <AlternatingRowStyle BackColor="White" />
                                <Columns>
                                    <asp:TemplateField HeaderText="Select">
                                        <HeaderTemplate>
                                            <asp:CheckBox ID="chkdetails" runat="server" />
                                            All
                                        </HeaderTemplate>
                                        <ItemTemplate>
                                            <asp:CheckBox ID="chk2" runat="server" />
                                        </ItemTemplate>
                                    </asp:TemplateField>
                                    <asp:BoundField DataField="emp_fullname" HeaderText="Employee" />
                                    <asp:BoundField DataField="EMP_ID" HeaderText="EMP ID" />
                                    <asp:TemplateField HeaderText="Assigned Leave">
                                        <ItemTemplate>
                                            <asp:DropDownList ID="CmbEmpLeave" runat="server" CssClass="col-md-12 form-control">
                                            </asp:DropDownList>
                                        </ItemTemplate>
                                    </asp:TemplateField>
                                    <asp:TemplateField HeaderText="Days">
                                        <ItemTemplate>
                                            <asp:TextBox ID="txtDays" CssClass="col-md-12 form-control" runat="server"></asp:TextBox>
                                        </ItemTemplate>
                                    </asp:TemplateField>
                                    <asp:TemplateField HeaderText="Date Type">
                                        <ItemTemplate>
                                            <asp:DropDownList ID="CmbDateType" CssClass="col-md-12 form-control" AutoPostBack="true" runat="server" OnSelectedIndexChanged="CmbDateType_SelectedIndexChanged">
                                                <asp:ListItem Text="Select Date Type" Value="0" Selected="True" />
                                                <asp:ListItem Text="English" Value="1" />
                                                <asp:ListItem Text="Nepali" Value="2" />
                                            </asp:DropDownList>
                                        </ItemTemplate>
                                    </asp:TemplateField>
                                    <asp:TemplateField HeaderText="Month">
                                        <ItemTemplate>
                                            <asp:DropDownList ID="CmbMonth" runat="server" CssClass="col-md-12 form-control">
                                            </asp:DropDownList>
                                        </ItemTemplate>
                                    </asp:TemplateField>
                                </Columns>
                                <EditRowStyle />
                                <FooterStyle BackColor="#507CD1" Font-Bold="True" ForeColor="White" />
                                <HeaderStyle BackColor="#507CD1" Font-Bold="True" ForeColor="White" />
                                <PagerStyle BackColor="#2461BF" ForeColor="White" HorizontalAlign="Center" />
                                <RowStyle BackColor="#EFF3FB" />
                                <SelectedRowStyle BackColor="#D1DDF1" Font-Bold="True" ForeColor="#333333" />
                                <SortedAscendingCellStyle BackColor="#F5F7FB" />
                                <SortedAscendingHeaderStyle BackColor="#6D95E1" />
                                <SortedDescendingCellStyle BackColor="#E9EBEF" />
                                <SortedDescendingHeaderStyle BackColor="#4870BE" />
                            </asp:GridView>
                        </div>
                    </div>
                </div>
            </ContentTemplate>
        </asp:UpdatePanel>
        </form>

Code

protected void Page_Load(object sender, EventArgs e)
{
    if (!IsPostBack)
    {
        loadDepartment();
    }
}

public void loadDepartment()
{
    DataTable dt = getDepartment();
    CmbDepartment.DataSource = dt;
    CmbDepartment.DataTextField = "DEPT_NAME";
    CmbDepartment.DataValueField = "DEPT_ID";
    CmbDepartment.DataBind();
    CmbDepartment.Items.Insert(0, "Select Department");
}

protected void CmbDepartment_SelectedIndexChanged(object sender, EventArgs e)
{
    string dept_id = CmbDepartment.SelectedValue;
    DataTable dt = getEmployeeListByDepartmentId(dept_id);
    GridView1.DataSource = dt;
    GridView1.DataBind();
}

protected void GridView1_RowDataBound(object sender, GridViewRowEventArgs e)
{
    if (e.Row.RowType == DataControlRowType.DataRow)
    {
        DropDownList CmbEmpLeave = (DropDownList)e.Row.FindControl("CmbEmpLeave");

        int emp_id = Convert.ToInt32(e.Row.Cells[2].Text);
        DataTable dtP = getleave_emp(emp_id);
        CmbEmpLeave.DataSource = dtP;
        CmbEmpLeave.DataTextField = "Leave_name";
        CmbEmpLeave.DataValueField = "leave_id";
        CmbEmpLeave.DataBind();
        CmbEmpLeave.Items.Insert(0, "Select");
        CmbEmpLeave.Items[0].Selected = true;
        CmbEmpLeave.Items[0].Attributes["disabled"] = "disabled";
    }
}

protected void CmbDateType_SelectedIndexChanged(object sender, EventArgs e)
{
    GridViewRow row = (sender as DropDownList).NamingContainer as GridViewRow;
    string ssss = (sender as DropDownList).SelectedValue;
    DataSet ds;
    if (ssss == "1")
    {
        ds = GetData("1");
    }
    else
    {
        ds = GetData("2");
    }
    DropDownList CmbMonth = row.FindControl("CmbMonth") as DropDownList;
    CmbMonth.DataSource = ds;
    CmbMonth.DataTextField = "MONTH_Name";
    CmbMonth.DataValueField = "MONTH_ID";
    CmbMonth.DataBind();
}

private DataTable getDepartment()
{
    DataTable dt = new DataTable();
    dt.Columns.AddRange(new DataColumn[]
    {
        new DataColumn("DEPT_ID"),
        new DataColumn("DEPT_NAME")
    });
    dt.Rows.Add(1, "IT");
    dt.Rows.Add(2, "CS");
    dt.Rows.Add(3, "Admin");

    return dt;
}

private DataTable getEmployeeListByDepartmentId(string dept_id)
{
    DataTable dt = new DataTable();
    dt.Columns.AddRange(new DataColumn[]
    {
        new DataColumn("EMP_ID"),
        new DataColumn("emp_fullname"),
        new DataColumn("dept_id")
    });
    dt.Rows.Add(1, "Name 1", 1);
    dt.Rows.Add(2, "Name 2", 3);
    dt.Rows.Add(3, "Name 3", 3);
    dt.Rows.Add(4, "Name 4", 2);
    dt.Rows.Add(5, "Name 5", 1);
    dt.Rows.Add(6, "Name 6", 1);
    return dt.Select("dept_id='" + dept_id + "'").CopyToDataTable();
}

private DataTable getleave_emp(int emp_id)
{
    DataTable dt = new DataTable();
    dt.Columns.AddRange(new DataColumn[]
    {
        new DataColumn("leave_id"),
        new DataColumn("Leave_name"),
        new DataColumn("EMP_ID")
    });
    dt.Rows.Add(1, "Leave 1", 1);
    dt.Rows.Add(2, "Leave 2", 3);
    dt.Rows.Add(3, "Leave 3", 2);
    dt.Rows.Add(4, "Leave 4", 2);
    dt.Rows.Add(5, "Leave 5", 1);
    dt.Rows.Add(6, "Leave 6", 3);
    dt.Rows.Add(7, "Leave 7", 4);
    dt.Rows.Add(8, "Leave 8", 5);
    dt.Rows.Add(9, "Leave 9", 6);
    dt.Rows.Add(10, "Leave 10", 4);
    dt.Rows.Add(11, "Leave 11", 5);
    dt.Rows.Add(12, "Leave 12", 6);
    return dt.Select("EMP_ID=" + emp_id).CopyToDataTable();
}

private DataSet GetData(string language)
{
    DataSet ds = new DataSet();
    DataTable dtEnglish = new DataTable();
    dtEnglish.Columns.AddRange(new DataColumn[]
    {
        new DataColumn("MONTH_ID"),
        new DataColumn("MONTH_Name")
    });
    dtEnglish.Rows.Add(1, "Baishakh");
    dtEnglish.Rows.Add(2, "Jestha");
    dtEnglish.Rows.Add(3, "Ashadh");
    dtEnglish.Rows.Add(4, "Shrawan");
    dtEnglish.Rows.Add(5, "Bhadra");
    dtEnglish.Rows.Add(6, "Ashwin");
    dtEnglish.Rows.Add(7, "Kartik");
    dtEnglish.Rows.Add(8, "Mangsir");
    dtEnglish.Rows.Add(9, "Poush");
    dtEnglish.Rows.Add(10, "Magh");
    dtEnglish.Rows.Add(11, "Falgun");
    dtEnglish.Rows.Add(12, "Chaitra");

    DataTable dtNepal = new DataTable();
    dtNepal.Columns.AddRange(new DataColumn[]
    {
        new DataColumn("MONTH_ID"),
        new DataColumn("MONTH_Name")
    });
    dtNepal.Rows.Add(1, "वैशाख");
    dtNepal.Rows.Add(2, "ज्येष्ठ");
    dtNepal.Rows.Add(3, "आषाढ़");
    dtNepal.Rows.Add(4, "श्रावण");
    dtNepal.Rows.Add(5, "भदौ");
    dtNepal.Rows.Add(6, "आश्विन");
    dtNepal.Rows.Add(7, "कात्तिक");
    dtNepal.Rows.Add(8, "मार्गशीर्ष");
    dtNepal.Rows.Add(9, "पौष");
    dtNepal.Rows.Add(10, "माघ");
    dtNepal.Rows.Add(11, "फाल्गुण");
    dtNepal.Rows.Add(12, "चैत्र");

    ds.Tables.Add(language == "1" ? dtEnglish : dtNepal);
    return ds;
}

Screenshot