All appointments made under sections 737.15 and 737.16 of the Revised Code shall be for a probationary period of six months’ continuous service, and none shall be finally made until the appointee has satisfactorily served his probationary period. At the end of the probationary period the mayor shall transmit to the legislative authority of the village a record of such employee’s service with his recommendations thereon and he may, with the concurrence of the legislative authority, remove or finally appoint the employee.