Two conservative organizations asked the Federal Election Commission yesterday to investigate what they described as dozens of apparent election-law violations by the Congressional Black Caucus-Political Action Committee.

Formal complaints were filed by the Washington Legal Foundation and the Fund for a Conservative Majority in connection with alleged shortcomings in the Black Caucus PAC's financial reports and in a controversial fund-raising appeal that the PAC sent out last month.

The April 14 mailing, which went out on stationery bearing a fictitious address, asked for $5,000 contributions from other PACs to help stem "a major push . . . now under way to . . .limit the growth of political action committees as we now know them."

The only major effort under way to control PAC spending is a bill backed by Common Cause, the self-styled citizens' lobby, and introduced on April 12 by Rep. David R. Obey (D-Wis.).

It has more than 100 co-sponsors, including five members of the CBC-PAC, Rep. William L. Clay (D-Mo.), the chairman; Rep. Louis Stokes (D-Ohio), the treasurer, and Reps. Parren J. Mitchell (D-Md.), Ron Dellums (D-Calif.) and John Conyers Jr. (D-Mich.).

The Washington Legal Foundation's director of litigation, Paul D. Kamenar, also named Stokes and Clay, who was the original treasurer of CBC-PAC, in his complaint because "the treasurer of each political committee is responsible for the proper accounting and reporting of receipts and disbursements."

Clay could not be reached for comment.

Stokes, who is chairman of the House Ethics Committee, said through an aide that he would address his response to the FEC "if and when" he receives any official communication from it.

"In essence," Kamenar charged, "the Congressional Black Caucus has apparently formed this political action committee and is running that PAC out of the Congressional offices of Congressman William Clay . . . . "

The complaint said this was evident from the financial reports of the committee through 1982, which showed nearly $33,000 in income but "NO expenditures for any office rent, office supplies and equipment . . . or telephones."

In addition, the Washington Legal Foundation said, the year-end report for 1982 showed a payment of $250 to Anise Jenkins, a legislative aide to Clay, for bookkeeping and accounting services, and listed as her address Clay's House office.

The chairman of the Fund for a Conservative Majority, Robert Heckman, also named the Black Caucus in his complaint, saying it should have been listed as a "connected" organization when CBC-PAC registered as a political committee.

The Washington Legal Foundation said CBC-PAC's April 14 appeal showed "a particularly egregious violation" in failing to state who paid for the mailing and whether it was authorized by any candidate or candidate's committee.