All original appointments to nonexempt positions in the City service shall be for a probationary period of six months, except that in the case of police officers the probationary period shall be one year. If at any time during such probationary period the appointing officer shall find the appointee unsatisfactory, he may dismiss such probationer and ask for the certification of new applicants. In case of such dismissal, the probationer, if he had civil service status in another position prior to his appointment to the position from which he is dismissed, shall automatically be restored to his former position; in other cases he may, in the discretion of the Civil Service Board, be reinstated on the eligible list if, after due inquiry, the Board deems him worthy of such reinstatement. If, at the end of the probationary period, the appointing authority has found the services of the appointee satisfactory, he shall so notify the Board and the probationer shall thereupon forthwith come under the merit system. The appointing officer may in his discretion extend the probationary period of any employee for one six-month period, provided that he shall so notify the Board and furnish the Board with a complete statement of his reasons for taking such action.