No, you don't need to include the tax return. You only need to mail the check along with the 1040-V payment voucher. Make your check or money order payable to “United States Treasury.
The payment voucher should be included with your printed tax return. Here is a link to the voucher https://www.irs.gov/pub/irs-pdf/f1040v.pdf. The mailing instructions can be found on page 2 of the form.
As an alternative you can pay online instead at https://www.irs.gov/payments.