Banking issues continued to get the attention of Maryland legislators last week in Annapolis, with the introduction of bills on unclaimed deposits and the return of canceled checks to customers.

Del. Stewart Bainum (D-Montgomery) has proposed comprehensive legislation on the unclaimed deposits issue. "There are $300 million worth of unclaimed assets, and the banks are obviously making money on it," he told the House Economic Matters Committee.

His bill would shorten to five years the period during which banks and other financial institutions can hold onto deposits that are unclaimed by depositors. (A 1975 law established a 12-year time limit. After that time, the funds are turned over to the state.) By reducing the time limit on this point, the state would get between $5 million and $15 million of the unclaimed deposits and other assets, depending on which one of several bills wins final approval.

Similar legislation has died in previous sessions, but Del. Frederick Rummage (D-prince George's), the committee chairman, said he expects approval this year.

Del. Patricia Sher (D-Montgomery) last week introduced a separate bill that would require banks and thrift institutions to return canceled checks to customers. Under the complex variety of checking plans now offered by the region's financial institutions, some banks and S&Ls are keeping canceled checks and mailing transaction summaries to customers in an effort to save costs on processing and mailing.

Sher's bill would premit this practice only where customers have agreed in advance, which some institutions already are doing. In addition, her bill would prevent the institutions from charging a fee to get a copy of a check, which some banks and S&Ls are doing for customers who do not get their checks back.

In other legislative action last week, Maryland commuters who travel to work on railroads in the Baltimore and Washington area -- but who face a loss of service with the projected absence of state aid -- told a hearing that federal help is available for the threatened rail lines if the state will ask for it.

The Maryland Department of Transportation has said service on Consolidated Rail Corp.'s Baltimore -Washington and Chessie System's Burnswick-Washington lines -- which the state subsidizes -- would end when leased rail cars have to be returned to New Jersey, which could be as early as July.

But commuters testifying on a bill that would establish permanent rail subsidies told the House Ways and Means Committee all the state has to do for financial help is to ask the federal government. "They would love to help us, but the state has to ask for the capital grant," said Stan Meiburg, a spokesman for the commuter group. "They need the basic request from the governor."

The federal Transportation Department will pay for 80 percent of certain projects under the Urban Mass Transportation Act. State officials say the cost of new equipment for the Conrail lines would be about $33 million.

Maryland currently pays New Jersey $500,000 a year to lease rail cars. Officials have said commuters would be able to use Chessie Baltimore-Union Station trains if the Conrail routes are discontinued. The House bill provides for the state Transportation Department's revenue account to pay for at least 50 percent of the commuter lines' annual deficit.

If only half the commuters who ride Conrail were forced to drive, they would consume an additional 348,000 gallons of gas a year, Meiburg said. In addition, he said, it would hurt commuters who work near the Baltimore-Washington International Airport, the site of a new, $3.5 million Amtrak station.

Rolf Schmitt, another member of the commuters group, said the Chessie trains (operated by a subsidiary, the Baltimore & Ohio) are not as convenient as Conrail and would not serve as adequate substitutes.

Given the Reagan administration's plans to cut the federal budget, however, it is unlikely that federal money will be available just for the asking. Indeed, Maryland and other states already are faced with a loss of potential aid for maintaining little-used freight rail routes. U.S. Office of Management and Budget Director David Stockman's "black book" of budget cuts calls for elimination of the Local Rail Service Assistance Program, which provides funds to states to support service on sparsely used branch lines.

The program is intended to cushion shippers from the effects of potential or actual rail line abandonments.

This week's business-related committee hearings in the Maryland and Virginia General Assemblies: MARYLAND SENATE

Tuesday: Finance Committee hearings on bills pertaining to health insurance for state employes and the merit system, 10 a.m., Presidential Wing, James Office Bldg.

Judicial Proceedings Committee to consider legislation relating to mortgages, 10 a.m., Room 300, James Office Bldg.

Wednesday: Budget and Taxation Committee hearings on energy saving device program legislation, 3:30 p.m., Room 100, James Office Bldg.

Economic Affairs Committee hearings on bills related to health insurance, 10 a.m., Room 200, James 1office Bldg.

Thursday: Economic Affairs Committee to consider small business assistance legislation, 10 a.m., Room James Office Bldg. MARYLAND HOUSE

Tuesday: Economic Matters Committee considers several insurance-related bills, 1 p.m., Room 150, Lowe Office Bldg.

Ways and Means Committee hearings on tax-related legislation, 1:30 p.m., Room 113, Lowe Office Bldg.

Wednesday: Constitutional and Administrative Law Committee hearings on minority business frauds legislation, 1 p.m., Room 140, Lowe Office Bldg.

Economic Matters Committee hearings on bills pertaining motor vehicle rentals, life insurance, real estate commission membership and Maryland Savings-Share Insurance Corp. membership, 1 p.m., Room 150, Lowe Office Bldg.

Thursday: Economic Matters Committee hearings on legislation having to do with insurance, passbook loans and mortgage assumability, 1 p.m., Room 150, Lowe Office Bldg.

Ways and Means Committee to consider tax-related legislation, 1:30 p.m., Room 110, Lowe Office Bldg. Virginia Senate (Standing Committees)

Monday: Agriculture, Conservation and Natural Resources Committee, 9 a.m., Senate Room A, General Assembly Bldg.

Commerce and Labor Committee, 2 p.m., Senate Room B, General Assembly Bldg.

Tuesday: Finance Committee, 10 a.m., Senate Room B, General Assembly Bldg.

Wednesday: Finance Committee, 10 a.m., Senate Room B, General Assembly Bldg.

Thursday: Transportation Committee, 2 p.m., Senate Room B, General Assembly Bldg. VIRGINIA HOUSE (Standing Committees)

Monday: Finance Committee,one half hour after adjournment, Room D, General Assembly Bldg.

Appropriations Committee, Monday through Friday, 45 minutes after adjournment, Appropriations Room, General Assembly Bldg.

Tuesday: Corporations, Insurance and Banking Committee, 10 a.m., Room 4, Capitol.

Health, Welfare and Institutions Committee, 9:30 a.m., Room C, General Assembly Bldg.

Wednesday: Agriculture Committee, 3 p.m., Room 2, Capitol. Conservation and Natural Resources Committee, 10 a.m., Room 4, Capitol.

Finance Committee, one half hour after adjournment, Room D, General Assembly Bldg.

Labor and Commerce Committee; 10 a.m., Room 2, Capitol.

Thursday: Corporations, Insurance and Banking Committee, 10 a.m., Room 4, Capitol.

Health, Welfare and Institutions, 9:30 a.m., Room C, Capitol.