As District officials began to defend their proposed $1.5 billion 1982 city budget on Capital Hill yesterday, they found members of Congress ready with questions about the size of the District's police department and the quality of the city's books after the first full District government audit in history.

During a hearing before the House District Appripriations subcommittee, Rep. William H. Natcher (D-Ky.), who last year persuaded Congress to mandate that the city hire more than 200 additional police officers, sharply questioned Mayor Marion Barry on the city's failure to increase the size of the force to that level.

"Isn't it time to just say you've made a mistake with this?" Natcher asked Barry. "Haven't you made a mistake with it, Mr. Mayor?"

Barry told Natcher that his recently announced program to reduce crime in the District calls for adding 75 officers to the force, which now has a uniformed strength of 3,631. But even the addition of those officers would be offset partially by reductions already planned for 1982, and would still leave the size of the force about 200 short of the 3,880 officers mandated by Congress.

"He and I both agree that the city ought to be safe," Barry said of Natcher after the subcommittee meeting. "The difference is that I have to find the money and make the sacrifices and he doesn't.

"More than likely they'll put another requirement on us this year, and we'll just see what we can do," Barry said.

Subcommittee chairman Julian Dixon (D-Calif.) questioned the mayor about discrepancies reported between 1980 expenditures reported by the city and those reported by the independent accounts, Arthur Andersen & Co. and Lucas, Tucker & Co., which recently finished the first audit of the city's books in history. City officials reported last week that the discrepancies, most of them not yet resolved, have made it impossible for the city to know precisely how much its departments spent last year.

Barry blamed the problem on the haste with which the final phases of the audit were completed.

"Part of our problem is that we had a Feb. 1 deadline to get the audit done," Barry sid. "It was touch and go for a while." He said financial officials of the various District agencies should have had the opportunity to sit down with the auditors and resolve the discrepancies before the document was released, but there was not enough time to do so.

"The auditors put their emphasis on the overall numbers," Barry said. "They really don't certify that what's behind those numbers is really behind those numbers."

The apperance of Barry, City Council Chairman Arrington Dixon and a host of other city financial officials before the House subcommittee yesterday kicks off nearly three weeks of department-by-department hearings into the District budget.