As you don't show much of your code, is is difficult to give any specific solution.
You code try to divide your code into two different parts, Select and Update.
At least it will be easier to find out which connection it is that throws the exception.
Also consider not to use SELECT * as it will give give you more data that you might need. In this case you might only need the primary key of the table, but it is difficult to say with so very little information.
DataTable dtResult = new DataTable();
using (SqlConnection SelectConnection = new SqlConnection(connectionString))
SqlDataAdapter da = new SqlDataAdapter("Select * From A", SelectConnection);
using (SqlConnection UpdateConnection = new SqlConnection(connectionString))
SqlCommand updateCommand = new SqlCommand();
updateCommand.Connection = UpdateConnection;
foreach (DataRow dr in dtResult.Rows)