Cambridge, after six months of bickering, still has no police chief.

The situation has been complicated by what a high city official called Civil Service Commission "politicking and favoritism." It started in April when Police Chief John King retired. Four police captains shortly after took a Civil Service examination for the post.

From the results of the exam, the City Manager was to appoint a police chief from the first three. When the Civil Service commission released the grades, the order was: Edward J. Maher with top grade, Joseph Linnehan second, Patrick F. Ready third, and Patrick F. McCarthy last.

McCarthy, who automatically loses claim to the chiefship, appealed to the Civil Service Director, who in turn up-held the grades of the original exam.

Going over the Director's head, McCarthy appealed to the Civil Service Commission directly. And yesterday, in a move that baffled city officials, the Civil Service Commission by a vote of three to one, upgraded McCarthy. Now the line-up stands: 1. Patrick F. McCarthy, 2. Edward J. Maher, 3. Patrick F. Ready, and 4. Joseph Linnehan.

As soon as the Civil Service Commission announced the new scores, Maher engaged an attorney to press his case for first place in the courts.

Unless Maher can obtain an injunction, the City Manager will have the job of choosing a chief by October 7, the legal deadline.