Northern Virginia last week became the first jurisdiction in the Washington area to begin inspecting automobile exhaust systems in compliance with a controversial federal mandate that Maryland legislators are threatening to ignore because of its cost and inconvenience.

The program of mandatory inspections, required here and in 37 other metropolitan areas found by the federal Environmental Protection Agency to have high concentrations of automobile-caused smog, officially begins in Virginia in 1982, when the owners of 500,000 Northern Virginia cars and light trucks will be required to have their vehicles' tailpipes inspected as part of their registration renewal.

To avoid a post-New Year's Day onslaught at the inspection stations -- police expect 33,000 cars to be inspected in January alone -- the program began last week at scattered sites.

Officials in the District of Columbia and Maryland do not intend to begin the inspections until 1983. There has been no change in those plans in Washington, where the tailpipe inspections will simply be included along with regular annual car inspections, according to a spokesman for the city's Motor Vehicle Administration.

But in Maryland, where the emissions inspections are required for Baltimore and its suburbs as well as Montgomery, Prince George's and Howard counties, some state legislators are now balking at a program that they say is expensive, excessive and a burden on the state's voting, tax-paying motorists.

Gov. Harry Hughes, a longtime advocate of auto inspections for cleaner air, has already signed a contract with a Palo Alto, Calif., firm to build 10 inspection stations around the state. That company, Systems Control Inc., has already begun buying property for the stations so the program can begin in January 1983.

But now Maryland delegates and senators have filed bills in advance of the coming January session that would delete all money for the program from the state's budget. Opponents of the inspections cite a variety of reasons for killing the program now, including the $9 fee to motorists, the chance that the Reagan administration will alter the Clean Air Act, which requires metropolitan areas to reduce smog, and the philosophy of a program that puts the burden of clean air on the driving public and not heavy-polluting industries.

Yesterday, three legislators took their complaint to court, filing a suit in Annapolis that contends the auto emissions program is unconstitutionally discriminatory because it applies only to the state's most populous areas.

Anne Arundel County Circuit Judge Nathaniel Hopper issued a "show cause" order requiring the state to explain why he should not issue a permanent injunction against further expenditures for the emissions program.

Maryland supporters of the inspection program view these last-minute reservations as a case of election-year politicking by legislators who see a chance to score points on a popular deregulation issue. Any change in the law now could end up costing the state money, they argue, since the contract signed with Systems Control is binding.

"Trying to undo the law at this point is a little like trying to squeeze toothpaste back into the tube," said Sen. Howard A. Denis (R-Montgomery). "Anyone who reads the contract the governor signed would know the penalty for withdrawing from the contract is so prohibitively high that it would cost the state millions."

In many ways the political squabble over clean air in Maryland is a replay of a decade of national debate over how far the federal government should go in trying to clean up America's dirty air. The much-amended and much-abused Clean Air Act passed Congress in 1970, but since then opponents of federal regulation have tried to dismantle it.

Under the provisions of the act, the EPA can withold public works funds to states that don't begin emission inspections. It was under this threat that both the Maryland and Virginia legislatures approved inspection programs.

Now local politicians, aware of the changing mood in Washington, are openly questioning the logic of proceeding with the program. The threat of a federal fund cut no longer seems as ominous from a White House that has targeted the Clean Air Act as inflationary and excessive.

President Reagan originally proposed a detailed revision of the law, but then backed off, essentially leaving it for now to Congress to make specific changes.

In Virginia, Del. Mary A. Marshall (D-Arlington) said she sponsored a "really rotten law" creating the inspections program in the state only so that Virginia wouldn't lose $350 million in federal highway funds. Now she said she is considering introducing legislation during the next session that would raise the vehicle inspection fee but would make emissions inspections voluntary, with funds from the program going to subsidize Metro.

In Maryland, Del. Timothy F. Maloney (D-Prince George's) said, "Can you picture Ronald Reagan coming in and cutting out federal highway funds because we don't comply with emissions standards? Everybody is banking on the administration and Congress to do something with the Clean Air Act next year."

Unlike Maryland, Virginia and the District of Columbia already have mandatory yearly car inspections, so the emissions testing will be just one more item on an annual checklist.

Virginia State Police said that cars and light trucks -- except diesels -- manufactured in the last eight years and registered in every Northern Virginia jurisdiction but rural Loudoun County, must submit to annual inspections in order to receive new vehicle registrations. Inspections cost $3.50 and are performed at licensed inspection stations.