Congress completed action on the District of Columbia's fiscal 1981 budget last night when the Senate approved the measure without opposition and sent it to President Carter for his signature.

The bill provides $1.5 billion in operating funds for the fiscal year, which began Oct. 1, along with a public works construction program totaling $221 million.It is supported in part by a record federal payment, chiefly in lieu of taxes on federally occupied lands in the city, of $295.4 million.

In following Tuesday's House action approving a report by a conference committee that reconciled differing House and Senate versions, the Senate accepted a House demand that the District hire about 200 police officers that Mayor Marion Barry contends are not needed. About $6 million was added to the budget to pay them.

The budget also provides funds to permit the city to raise wages for its employes by 5 percent, less then the 9.1 percent granted to federal workers. Unions representing most city employes are challenging the lower figure.

Congress also added $1.2 million to the city school budget of $275.6 million to help offset reductions in the number of classroom teachers.

As finally approved, the budget provides, among other things, $3.3 million to pay court judgments won by antiwar protesters arrested by city police during mass May Day demonstrations at the Capitol in 1971; grants $719,000 to finance operations of the city,s advisory neighborhood commissions, a rise of $94,000 from last year, and omits $1 million the city had sought to begin a limited rent supplement program for improverished tenants.