Baltimore Mayor William Donald Schaefer announced tonight that Maryland Senate President Melvin A. Steinberg will be his running mate in the race for the Democratic gubernatorial nomination.

Schaefer introduced Steinberg on the steps of the Baltimore County Courthouse to a crowd of 200 that included dozens of state and local officeholders as "a man who makes things happen, a man who is guided by what he thinks is right, not by what is politically expedient."

Steinberg, whose acceptance of the lieutenant governor's candidacy puzzled many who know his fondness for playing on center stage in the legislature, said he agreed to join the Schaefer ticket because he shares the mayor's vision of making Maryland "the best state in America."

Steinberg, 52, has represented the Pikesville area of Baltimore County in the Senate for 20 years, and has served as president of the upper chamber of the General Assembly since 1983. His agreement to be Schaefer's running mate had been expected since last week.

Though not well known outside of his home district, Steinberg is regarded by Schaefer forces as a strong addition to the ticket who will solidify the mayor's already formidable appeal in this county, as well as among Jewish voters. He is also being touted as someone who would strengthen Schaefer's rule in Annapolis if the ticket is successful, particularly in its relations with the legislature.

Schaefer's Democratic opponent, Attorney General Stephen H. Sachs, who also is Jewish, said the mayor's choice of Steinberg "presents a very clear contrast" with his own ticketmate, U.S. Rep. Parren J. Mitchell, the liberal black congressman from West Baltimore.

"We represent a more open politics; they represent a more closed politics," said Sachs. "We represent the politics of the community; they represent the politics of the clubhouse."

In picking Steinberg, who has been an iron-willed but genial Senate president, Schaefer has opted for a lieutenant governor candidate who can challenge, if not match, the stature that Mitchell brings to Sachs, and who promises to be a forceful campaigner.

"What Sachs did in picking up Mitchell was a great stroke," said state Sen. John C. Coolahan (D-Baltimore County). "But with Schaefer now picking up Steinberg, there's a checkmate."

Coolahan, perhaps Schaefer's most vociferous critic in Annapolis over the years, demonstrates the pulling power of Steinberg, at least in Baltimore County. Both Coolahan and Sen. Norman R. Stone Jr., also of Baltimore County, had been neutral in the governor's race, but are now expected to side with Schaefer.

Nonetheless, some political observers suggested that Steinberg does little to broaden the mayor's appeal and only reinforces his strengths in the race in which most surveys give him a 2-1 advantage.

"They [the Schaefer camp] are totally ignoring the political aspects of the race," said Keith Haller, a Montgomery County-based pollster and political consultant. "Schaefer has more popularity in the Baltimore suburban jurisdictions than anywhere. Why does he need to go with a Baltimore County person?"

But the selection of Steinberg appeared to represent a desire on the part of Schaefer to look beyond the politics of winning the Sept. 9 Democratic primary to the task of governing.

In the course of several meetings with Steinberg over the past 10 days, Schaefer convinced him that he would enjoy a greater policy role than that practiced by the two lieutenant governors who have served the Democratic incumbent, Gov. Harry Hughes.

Under a Schaefer administration, said Steinberg, the No. 2 policy position would be held by the lieutenant governor and not the governor's chief of staff as has been the case under Hughes.

Some sources close to the Schaefer campaign predicted today that Steinberg would be an aggressive campaigner against Sachs, particularly on the issue of the attorney general's role in the state's savings and loan crisis.

Steinberg himself brings some savings and loan baggage to the Schaefer ticket. Steinberg was a key legislator during the period when the assembly deregulated the thrift industry, and a Washington Post poll, conducted in March, showed that 40 percent of those surveyed said they assign a "great deal" of blame for the savings and loan crisis to the legislature.