The department of job and family services shall enter into a contract with local hospitals for the provision of staff by the hospitals to meet with unmarried women who give birth in or en route to the particular hospital. On or before April 1, 1998, each hospital shall enter into a contract with the department of job and family services pursuant to this section regarding the duties imposed by this section and section 3727.17 of the Revised Code concerning paternity establishment. A hospital that fails to enter into a contract shall not receive the fee from the department for correctly signed and notarized affidavits submitted by the hospital.