In what may be his last confrontation with the D.C. City Council, Mayor Walter E. Washington has vetoed a bill that would require future mayors to submit the names of their proposed department heads to the council for confirmation.

The process would be similar to that followed by the president in choosing cabinet members, agency heads and judges, who must be confirmed by the Senate.

In objecting to adopting the procedures locally, the outgoing mayor sent the council a strongly worded veto contending it would both violate the city Home Rule Charter and be politically undesirable.

Washington's veto is likely to prove more symbolic than effective. The 13-member council passed the bill unanimously on Oct. 31 and can override the veto Tuesday if two-thirds of those who are present stick by their original position.

The meeting Tuesday is council's last scheduled session of the year.

Washington leaves office Jan. 2 and will be replaced by council member Marion Barry (D-At Large), who voted for the bill.

"After more than a decade as chief executive in the District of Columbia," the mayor said in his veto message, "I find myself completely at odds with the idea of diminishing the critical power of the chief executive of the District of Columbia to appoint the subordinate officers through which he exercises most of his authority."

Under existing law, which the city inherited from the decades before home rule, most department heads are career appointees, protected from arbitrary removal by federal civil service rules.

On the same day as the council passed the now-vetoed confirmation bill, it also enacted a new personnel law that will grant future mayors the right to appoint and remove department heads, including those now serving. That measure, recently signed by Washington and expected to go into effect early next year, makes n o mention of the confirmation process.

A council staff member said the confirmation measure was split off and made into a separate bill both to avert the risk of a mayoral veto of a combined personnel package, and to guard against a legal challenge to the confirmation process.

In his veto message, the mayor said the confirmation process "is defective on policy as well as purely legal grounds."

"Before the council began its consideration of a new personnel system . . . the office of the corporation counsel (the city's legal office) as well as the office of legal counsel of the U.S. Department of Justice advised that it was beyond the authority of the council under the District (Home Rule) Charter to subject mayoral appointees to council approval" with certain exceptions, the mayor wrote.

Exceptions include the heads of independent agencies, such as the D.C. Public Service Commission, and members of certain boards and commissions.

In mid-November, the council rejected five nominations by Washington to the Board of Trustes of the University of the District of Columboa, contending that Barry should make the appointments after taking office.

In another veto action, the council voted last week to override the mayor's veto of part of the proposed city budget for the 1980 fiscal year.

In enacting the budget bill, the council had rejected $2.1 million in various items, chiefly for the Department of Human Resources, that had been proposed by the mayor. The mayor vetoed the council action on those items. On a motion by Council Chairman Sterling Tucker, the council unanimously voted to override.

However, the council upheld the mayor in restoring $1.3 million in improvements to facilities at D.C. General Hospital.