A City Council committee last week approved legislation that would permit the Department of Transportation to begin staggered auto registrations beginning in April in an effort to avoid the crush of applications that snarls the agency each year.

The program, which would be phased in over two years at a cost of about $1 million, would result in some motorists having to renew their 1984 permits after only three months, according to a report by the committee on transportation and environmental affairs.

The bill gives the mayor and DOT full authority to redesign the city's system, which now requires that all vehicle registrations expire annually on March 31, regardless of when they are issued.

The proposed program, according to transportation director Thomas Downs, would help to streamline DOT's operations. DOT officials hope to provide "one-stop" registrations for owners who now must go to as many as six different stations to obtain routine permits.

About 75 percent of the city's 300,000 vehicles are reregistered each March. Despite the annual mail registrations that begin in February, DOT's offices are swamped by owners who register in person, often causing waits of up to two hours just before the deadline.

The first phase of the program would begin next March, when all permits would be granted for one year. Registrations granted in April or subsequent months through February 1984 would expire the same month the following year.

Beginning in March 1984, those who hold registrations that expire that month would be granted registrations for periods ranging from three months to 11 months -- at prorated fees. As these permits expired, motorists would register for full, one-year permits.

It was unclear last week how the department would decide which drivers would be given the shorter registrations.

All District of Columbia and U.S. government and Metro transit vehicles that now renew tags annually would get permanent tags under the proposed system.

The suggested changes are part of a plan that would increase the cost of registering most vehicles in the District. Mayor Marion Barry last week announced proposed legislation that would charge owners of most small cars $48 a year for registrations, compared to $35 now. Owners of larger cars, which now cost up to $76 to register, would pay $60 under the plan, which must be approved by the council.