Combining Insert/Update to one Procedure

CREATE PROCEDURE sp_Insert
	
	(
	@ID int,
	@Name char(20),
	@Mode char(20)
	)
	
AS
if @Mode='Insert in Employee'
Begin
	insert into Employee(Employee_ID,Employee_Name)values(@ID,@Name)
End
else if @Mode='Insert in Student'
Begin
    insert into Student(Student_ID,Student_Name)values(@ID,@Name)
End

	RETURN

private void Employee_Save_Click(object sender, EventArgs e)
       {
           SqlConnection conn = new SqlConnection(" ");
           conn.Open();
           SqlCommand cmd=new SqlCommand("SP_INSERT",conn);
           cmd.CommandType=CommandType.StoredProcedure;
           cmd.Parameters.AddWithValue("@ID",txtEmployeeID);
           cmd.Parameters.AddWithValue("@Name",txtEmployeeName);
           cmd.Parameters.AddWithValue("@Mode","Insert in Employee");
           cmd.ExecuteNonQuery();
           conn.Close();

       }
       private void Student_Save_Click(object sender, EventArgs e)
       {
           SqlConnection conn = new SqlConnection("")
           conn.Open();
           SqlCommand cmd = new SqlCommand("SP_INSERT", conn);
           cmd.CommandType = CommandType.StoredProcedure;
           cmd.Parameters.AddWithValue("@ID", txtStudentID);
           cmd.Parameters.AddWithValue("@Name",txtStudentName);
           cmd.Parameters.AddWithValue("@Mode", "Insert in Student");
           cmd.ExecuteNonQuery();
           conn.Close();
       }