Jail crowding, the District's serious drug problems and other criminal justice issues are expected to grab much of the attention of those working on District legislation in Congress this year.

Whether to build a new prison and where -- questions that in the past have pitted Mayor Marion Barry against the U.S. attorney's office, Hill Republicans and Northern Virginians -- is the most controversial of the city issues.

Also on the agenda in the 99th Congress are job training for prisoners, curbing truancy in schools and legislative solutions to drug problems.

The District will push to get authority to appoint local judges, prosecute cases and make parole decisions on all District offenders -- efforts that face uphill battles in Congress.

City officials had been hopeful of getting some of these increased home rule powers in the last Congress. But efforts came to an abrupt halt because of a serious constitutional problem that arose over the city's basic authority to govern itself.

That problem -- a result of a 1983 Supreme Court ruling -- was resolved in the final hours of the last Congress, so the city can go back to working on chipping away at congressional control over city functions.

The District has a complicated and sensitive relationship with Congress. Since home rule went into effect a decade ago, the city has been able to enact laws, but Congress retained oversight authority on local legislation. Congress also must approve, and can amend, the city's budget.

On money matters, the District will push an annual wish list item that predates home rule -- establishing a formula for the annual federal payment to the city in lieu of taxes, so city officials will not have to negotiate the amount each year as they try to plan their budget.

The city will make a case for ending congressional authority to rearrange its annual budget, and Congress may start debate on statehood for the District. But congressional experts, including supporters, do not expect these items to go very far in the next two years.

Plans for transferring control of St. Elizabeths mental hospital from the federal government to the District will come under congressional review as the city prepares to take over management in October 1987.

Sen. Arlen Specter (R-Pa.), chairman of the Senate subcommittee on District appropriations, has said he plans to press hard to build more prison space to deal with an expected jump in the District's prison population, whether or not the mayor requests federal land and money for this purpose.

Barry has resisted efforts to build more prison space, but recently, under pressure from Specter, he said he would not oppose it if money -- preferably federal funds -- could be found.

Pauline Schneider, the city's director of intergovernmental relations, said the mayor still wants an analysis done before any decisions are made and "not just get it prison expansion dumped on the city or forced on the city."

One congressional aide, however, predicted that "Barry will be pushed on prisons if he doesn't do it himself," and the aide added, "The city should get out in front on it."

Specter said he thought Congress could measure up to its responsibility to fund construction, and in the past two years as chairman he has shown the ability to add millions of dollars in federal funding to the District's budget for special projects.

One way to approach prison construction during a time of federal budget freezes and cutback proposals might be to include design money only the first year. Construction of a 1,000-bed prison would cost $40 million to $80 million by rough city estimates.

At a recent luncheon with reporters and editors at The Washington Post, Specter said he thought city officials were happy with the way the budget has been handled.

"I think the mayor is very pleased with the way it the budget process works. He brings us a budget, and we do not tamper with it much," the senator said. "In the two years I've been there, most of the suggestions have been add-ons to try to help them to explore areas where I think he needs a little bit of extra help."

But city officials chafe under congressional changes to their budgets, even when it means more money. They will argue this session for a formula to establish the amount of federal funds to be given to the city as one step toward budget autonomy. The fiscal 1985 federal payment was $425 million, and millions were added to subsidize St. Elizabeths and for a special criminal justice initiative and school programs added by Specter.

D.C. Del. Walter E. Fauntroy, a top-ranking member of the House District Committee, said the formula payment is something he will "seek seriously" in this Congress.

"If it is a fair formula, what we have gained by the special concessions of senators like Arlen Specter would probably be balanced off by things that we lose from time to time because of special interests that work against the District," Fauntroy said in a recent interview.

The incentive for the formula was muted last year by a surprisingly high $39 million increase in the federal payment proposed by the Reagan administration in its fiscal 1985 budget and approved without controversy by Congress.

But, illustrating the fickleness of the system, the advance word from the White House is that it wants no increase this year. Congressional aides said, however, that they believe a special subsidy of $25 million authorized for St. Elizabeths last year will be included in the president's budget.

Schneider said officials are working on a proposal to end congressional review of bond authorizations. Like other District legislation, bills authorizing the issuance of bonds for particular projects do not take effect until after a congressional review period of 30 legislative days, which can be as long as six months because of recesses and adjournments. This can complicate financial planning for projects.

The District will renew its attempts to transfer authority to appoint local judges from the president to the mayor. This was approved by the House in the last Congress, and key Republicans promised to back it, but no action was taken in the Senate.

The Reagan administration is not expected to back off its strong opposition to the plan, and supporters acknowledge that it will be difficult to get the proposal through Congress.

The city would like the D.C. Parole Board to have parole authority over the more than 1,000 District offenders who are housed in federal prisons and are subject to federal parole standards.

The House approved this change in the last Congress, but no action was taken in the Senate. Specter, in the meantime, blasted the city's parole board repeatedly for what he saw as lax standards of release and concentrated on getting the District to construct guidelines that probably would keep more prisoners in jail longer.

The District will press for ownership of RFK Stadium and the Employment Security Building at Sixth and Pennsylvania Ave. NW, which now houses the D.C. Department of Employment Services. Both are owned by the federal government.

No one expects statehood to pass soon, at least as long as there is a Republican majority in the Senate, but work has begun on making the proposed state constitution less controversial than the one that was submitted to the last Congress.

Fauntroy said he would like to put statehood to a test vote in 1986, after working on simplifying the constitution this year.

Meanwhile, Rep. Stewart B. McKinney (R-Conn.), the ranking Republican on the House District Committee, has said he wants to give the city the few remaining powers it lacks and abolish the District Committee.