Simmering discontent among D.C. City Council members over the leadership of Chairman Arrington Dixon boiled over yesterday when the council refused to approve Dixon's choice for a $50,112-a-year staff job.

After voting 7-to-6 against choosing a new chief lawyer and parliamentarian for the council, members accused Dixon during a 45-minute debate of failing to meet with them to decide a policy for council staff appointment. They also complained that Dixon sidetracked a bill he promised to consider that would slash top salaries far below the level proposed yesterday.

Even a member who sided with Dixon in yesterday's vote, David A. Clarke (D-Ward I), agreed with critics, asserting that "I don't think Mr. Dixon is exerting the proper leadership here, either."

The debate was by far the angriest since Dixon took office 16 months ago as the council's presiding officer.

Council members have been grumbling that Dixon has failed from the start of his term to consult them on key appointments and has treated top staffers as personal aides rather than as officials responsible to all 13 members. Some also have complained privately that Dixon has failed to adopt a clear legislative program for the council.

The council's own budget for the coming 1981 fiscal year also figured in yesterday's dispute. Dixon testified recently before Congress that the council hopes to add 18 persons to its 130 staff members. Betty Ann Kane (D-At-Large) said the council must be prepared, like any other city agency, to make reductions during the current financial crisis.

The staff appointment issue first erupted last month when Dixon nominated John P. Brown Jr. to fill a longstanding vacancy as secretary of the council -- its top administrative post -- at a $50,112-a-year salary.

Council members confirmed Brown only after Dixon agreed to reduce his starting pay by $10,000.

At the same time, five members introduced a bill to set a lid on council staff salaries at $37,500, the top pay level for council members. Dixon agreed to consider the bill promptly. But Polly Shackleton (D-Ward 3) and others said yesterday that he had failed to do so and also had refused to meet as often as requested on overall council staffing policies.

Two weeks ago, despite the proposed lid on staff pay, Dixon nominated Lawrence H. Mirel, 44, a lawyer now in private practice, to become general counsel to the council at a $50,112 salary. He was nominated to replace James M. Christian, a Dixon nominee who left recently to join a private law firm.

When Dixon called the nomination up for endorsement yesterday, Shackleton promptly moved to table it. Such a motion cannot be debated.Shackleton stressed that her move was aimed at Dixon, not at nominee Mirel.

In a roll call vote, Shackleton was joined by Betty Ann Kane (D-At-Large), Hilda Mason (Statehooe-At-Large), John L. Ray (D-At-Large), Wilhelmina J. Rolark (D-Ward 8), John A. Wilson (D-Ward 4) and Nadine P. Winter (D-Ward 6). Supporting Dixon were Clarke, Willie J. Hardy (D-Ward 7), Charlene Drew Jarvis (D-Ward 4), Jerry A. Moore Jr. (R-At-Large) and William R. Spaulding (D-Ward 5).

When Winter sought after the vote to get a parliamentary ruling on a proposed resolution dealing with council staffing, Dixon coldly informed her there was no general counsel to provide the information.

Ray said Barbara Mann, a lawyer from the general council's office who was seated next to Dixon, could provide the ruling. Dixon said Mann was serving as his own adviser, not the council's and indicated that he had no plan to appoint an acting general councel to serve until the Mirel nomination is resolved.

This set off another round of argument among Dixon, his supporters and his critics. Dixon also sought but failed to win council agreement yesterday for the appointment of Leonard C. Pryor, 29, as director of the Council's city budget review staff, at an unspecified salary. Dixon withdrew Pryor's nomination after Shackleton moved to table it.