Search TreeView Nodes using TextBox in ASP.Net

Here I have created sample that will help you out.

HTML

<div>
    Parents :<asp:DropDownList ID="ddlParents" runat="server" OnSelectedIndexChanged="ChangeChild"
        AutoPostBack="true">
    </asp:DropDownList>
    &nbsp;&nbsp;Childs :
    <asp:DropDownList ID="ddlChilds" runat="server" AppendDataBoundItems="true">
        <asp:ListItem Text="Select" Value="0" />
    </asp:DropDownList>
    <h3>
        Vehicle Details</h3>
    <hr />
    <asp:TreeView ID="TreeView1" runat="server" ImageSet="News" NodeIndent="15">
        <HoverNodeStyle Font-Underline="True" ForeColor="#6666AA" />
        <NodeStyle Font-Names="Tahoma" Font-Size="8pt" ForeColor="Black" HorizontalPadding="2px"
            NodeSpacing="0px" VerticalPadding="2px"></NodeStyle>
        <ParentNodeStyle Font-Bold="False" />
        <SelectedNodeStyle BackColor="#B5B5B5" Font-Underline="False" HorizontalPadding="0px"
            VerticalPadding="0px" />
    </asp:TreeView>
    <asp:TextBox ID="Txtfind" runat="server" BorderColor="#999999" BorderStyle="Solid"
        Style="margin-top: 0px; border-radius: 5px" Width="150px" BackColor="#CCCCCC"></asp:TextBox>
    <asp:Button ID="srch" runat="server" Text="Search" OnClick="Search_Click" />
</div>

Code

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

protected void ChangeChild(object sender, EventArgs e)
{
    DataTable dtChild = GetChildData(int.Parse(ddlParents.SelectedItem.Value));
    this.ddlChilds.Items.Clear();
    this.ddlChilds.DataSource = dtChild;
    this.ddlChilds.DataTextField = "Name";
    this.ddlChilds.DataValueField = "Id";
    this.ddlChilds.DataBind();
    this.ddlChilds.Items.Insert(0, new ListItem("Select", "0"));
}

private void PopulateTreeView(DataTable dtParent, int parentId, TreeNode treeNode)
{
    foreach (DataRow row in dtParent.Rows)
    {
        TreeNode child = new TreeNode
        {
            Text = row["Name"].ToString(),
            Value = row["Id"].ToString()
        };
        if (parentId == 0)
        {
            TreeView1.Nodes.Add(child);
            DataTable dtChild = this.GetChildData(Convert.ToInt32(child.Value));
            PopulateTreeView(dtChild, int.Parse(child.Value), child);
        }
        else
        {
            treeNode.ChildNodes.Add(child);
        }
    }
}

public DataTable GetParentData()
{
    DataTable dt = new DataTable();
    dt.Columns.AddRange(new DataColumn[2] { new DataColumn("Id", typeof(int)),
            new DataColumn("Name", typeof(string))});
    dt.Rows.Add(1, "Audi");
    dt.Rows.Add(2, "BMW");
    dt.Rows.Add(3, "Bugati");
    return dt;
}

public DataTable GetChildData(int vehicleTypeId)
{
    DataTable dt = new DataTable();
    dt.Columns.AddRange(new DataColumn[3] { new DataColumn("Id", typeof(int)),
            new DataColumn("Name", typeof(string)),
            new DataColumn("VehicleTypeId", typeof(int))});
    dt.Rows.Add(1, "Audi-100", 1);
    dt.Rows.Add(2, "BMW-Zx", 2);
    dt.Rows.Add(3, "Bugati-895", 3);
    dt.Rows.Add(4, "Audi-200", 1);
    dt.Rows.Add(5, "BMW-Zz", 2);
    dt.Rows.Add(6, "Bugati-800", 3);
    DataRow[] filteredRows = dt.Select("VehicleTypeId=" + vehicleTypeId);
    DataTable resultDt = dt.Clone();
    foreach (DataRow dr in filteredRows)
    {
        resultDt.ImportRow(dr);
    }
    return resultDt;
}

public void PopulateParents()
{
    DataTable dt = this.GetParentData();
    this.ddlParents.DataSource = dt;
    this.ddlParents.DataTextField = "Name";
    this.ddlParents.DataValueField = "Id";
    this.ddlParents.DataBind();
    this.ddlParents.Items.Insert(0, new ListItem("Select", "0"));
    this.PopulateTreeView(dt, 0, null);
}

protected void Search_Click(object sender, EventArgs e)
{
    if (!string.IsNullOrEmpty(Txtfind.Text))
    {
        TreeNode searchedNode = null;
        foreach (TreeNode node in TreeView1.Nodes)
        {
            searchedNode = SearchNode(node, Txtfind.Text);
            if (searchedNode == null)
            {
                foreach (TreeNode childNode in node.ChildNodes)
                {
                    searchedNode = SearchNode(childNode, Txtfind.Text);
                    if (searchedNode != null)
                        goto Here;
                }
            }
            else
            {
                break;
            }
        }
    Here:
        if (searchedNode != null)
        {
           searchedNode.Select();
           TreeView1.ExpandAll();           
           Txtfind.Text = "";
        }
        else
        {
            this.ClientScript.RegisterStartupScript(this.GetType(), "Not Found", "alert('Node " + Txtfind.Text + " not found');", true);
        }
    }
}

TreeNode SearchNode(TreeNode node, string searchText = null)
{
    if (node.Text == searchText) return node;

    TreeNode tn = null;
    foreach (TreeNode childNode in node.ChildNodes)
    {
        tn = SearchNode(childNode);
        if (tn != null) break;
    }

    if (tn != null) node.Expand();
    return tn;
}

Screenshot