If Senate President James Clark Jr. has his way, voters in Maryland will have a chance to abolish the office of lieutenant governor on the same day they choose someone to fill the office this year.

Testifying on his proposal to abolish the No. 2 office and make the secretary of state next in line of succession to the governor, Clark said today that the move would save the state about $250,000 annually.

"I've always felt this was an unnecessary expense," Clark told the Senate Constitutional and Public Law Committee. "We got along for a lot of years in Maryland without a lieutenant governor and I'm not sure we need one now."

If Clark's bill, or one introduced by Sen. Julian L. Lapides (D-Baltimore) that abolishes the office but makes the attorney general next in the line, is enacted, the question will be placed on the November ballot. If the proposal is approved then, the office will cease to exist at the end of the next term, in January 1987.

According to testimony today, nine states operate without a lieutenant governor and in three of them, the secretary of state is first in the line of succession.

Part of the reason there is interest in the bill has been the rancorous relationship between Gov. Harry Hughes and Lt. Gov. Samuel W. Bogley. The two men split over the issue of abortion even before being elected and, because of the rift, Bogley's job has been largely ceremonial.

Bogley, at the request of the governor's office, did not testify on the bill, but he said this afternoon he could see reasons for abolishing the office.

"If you are being forced to tighten up at lower levels of government, there's reason to look to higher levels for ways to cut back too. The man who acts as the governor's No. 2 man doesn't necessarily have to hold the title of lieutenant governor."

The office of lieutenant governor was established after former governor Spiro T. Agnew resigned to become vice president in 1969.