Two District of Columbia referendums -- one to legalize certain forms of gambling and the other to put the city on the path to statehood -- quietly became law yesterday, leaving city officials with the first voter-initiated legislation since home rule but no readily identifiable funds to put the laws fully into effect.

There were no brass bands and no fanfare to mark the expiration of the mandatory 30-day congressional review cycle for the two measures approved by voters last November -- despite the fact that the referendums laid the groundwork for potentially far-reaching and fundamental changes in the life styles of residents in the nation's capital and the operations of it local government.

The gambling referendum will authorize a city-run lottery and daily numbers game, similar to that operated in nearby Maryland, and permit gambling for charitable purposes. The statehood initiative provides for selection of delegates to a convention to draft a state constitution for the nation's capital that would later be put before the city's voters and possibly Congress.

Nevertheless, the cash-strapped city government has no money allocated in this year's or next year's budget for either initiative, and both will be costly to implement.

It is estimated that gambling would produce about $30 million a year for the District, but not until late 1982 at the earliest.

Until then, the city must still pay $15,000 a year to four members of the gambling control board, $18,000 a year to its chairman and $50,000 for the staff director.The gambling commission would also need a supporting staff, which would include a lawyer, clerks and someone to oversee the bingo and raffle games that become legal immediately.

The statehood initiative will cost about $750,000 -- including an estimated $400,000 for the convention alone -- and both supporters and city officials have said they are reluctant to seek the money from Congress, where opposition has been voiced to legal gambling in the nation's capital. The opposition faded only last week.

Council Chairman Arrington Dixon said on Monday that the city could find the money for the gambling initiative by reprogramming -- which is essentially diverting unspent funds originally allocated for some other purpose.

Also, the mayor has the authority to borrow money from the U.S. Treasury based on anticipated revenue.And the lottery equipment companies can usually be contracted on a pay-later basis, until the gambling revenue begins pouring in.

Financing the statehood initiative will prove a bit more difficult because it will not generate its own funds and can thus not be financed through cash anticipation loans.

Implementation of the gambling law officially begins today with the search for five members for the newly created D.C. Lotteries and Charitable Games Board. Mayor Marion Barry will move immediately to fill those positions, possibly as early as next week, according to his press secretary, Alan F. Grip.

Already the betting is on as to who will be appointed to the board, which has the power to decide what types of games will be operated here, which lottery equipment companies will win the lucrative contract to run the games, and how to select the grocery stores and liquor outlets that will be licensed to sell lottery tickets.

Barry has not made his choices known yet, but already those who were most involved in the D.C. Committee for Legalized Gambling, which spear-headed the citizens campaign to get the referendum approved, are angling for appointment.

Brant Coopersmith, the chairman of that committee, and Jerry Cooper, the Ward 1 Democratic Club chairman who also worked on the committee, have already expressed interest in seats on the board.

The statehood process could begin formally as early as this November, with the election of 45 delegates to a statehood constitutional convention -- five at-large delegates and five delegates elected from each of the city's eight wards.

The D.C. Statehood Initiative Committee, which pushed for passage of the measure, will be holding a citywide meeting in late April to prepare the city for the process and to encourage citizens to take out nominating petitions to run for statehood delegate, according to cochairman Edward Guinan.