You can use DataView for that.
First declare a Global DataTable. then store your all database value to that datatable.
Second declare a Global DataView.
Eg:-
static DataTable dtTable;
static DataView dvTable;
On Page Load save your all database value to DataTable.
Now perform your search option in that DataTable.
Eg:-
dvTable = new DataView(dtTable);
dvTable.RowFilter = "your filter query";
dropdown.DataSource = dvTable.ToTable();
dropdown.DataTextField = "your text field";
dropdown.DataValueField = "your value field";
dropdown.DataBind();
Hope you got it.
Happy Holi.