you need to specify which connection to use in sql command.
SqlCommand cmd= new SqlCommand("INSERT INTO Employee (Dept_Name, Dept_ID, Emp_Name) SELECT Dept_ID, Dept_Name FROM Department WHERE Dept_Name = ddlDeptName.SelectedValue ", con);
and also you haven't include parameters in your sql statement, it should be like below
INSERT INTO Employee (Dept_ID,Dept_Name) SELECT Dept_ID, Dept_Name FROM Department WHERE Dept_Name = @Dept_Name
since you have one parameter, you can set it as below
cmd.Parameters.AddWithValue("@Dept_Name", ddlDeptName.SelectedValue);