Sen. Charles McC. Mathias (R-Md.) has introduced a bill that would greatly strengthen President Reagan's hand in appointing District of Columbia judges and would allow city judges to live outside the District.

D.C. officials, who called the move a "slap at home rule," said yesterday they were not consulted about the bill, which several saw as a move by the Reagan administration to gain control over the local judicial appointment process. If enacted, it also would reverse a general trend toward giving the city more autonomy over its own affairs.

Under the independent powers granted the District under home rule in 1973, the seven-member D.C. Judicial Nomination Commission now sends the White House a list of three candidates for any vacancy on the D.C. Superior Court and the D.C. Court of Appeals. The president has 60 days to choose one of those candidates and send the nominee to the Senate for confirmation.

If the president does not act within that time, the commission has the power to select its own nominee from the list and forward the nomination directly to the Senate. However, since the commission was created, such a situation has not occurred.

Under the bill proposed by Mathias, there would be no time limit for presidential action. The president could also request additional names until the commission sent him someone he was willing to nominate, and the seat would remain vacant until then.

In addition, the commission now must pick candidates who either live in the District of Columbia or would move to the city shortly after their appointment. Under Mathias' bill, candidates still would be required to be members of the D.C. Bar, but would only have to live within 20 miles of the District to be eligible.

The bill would also overturn a July federal court ruling that said Reagan exceeded his authority when he attempted to replace commission member William A. Borders Jr. with local attorney Philip A. Lacovara. The bill states that commission members appointed by the president would serve at the president's pleasure.

Borders was indicted last month by a federal grand jury in Miami on charges that he conspired with a federal judge there to accept a $150,000 bribe. Borders has temporarily withdrawn from commission activities pending the outcome of his case.

Of the remaining members of the commission, two are appointed by the D.C. Bar, two by the mayor, one by the D.C. City Council and one by the chief judge of the federal court here. That situation would remain the same under the bill, although the chief judge of the federal court, who now must appoint a sitting or retired federal judge to the commission, would not be restricted to appointing federal judges to that seat on the commission.

Mayor Marion Barry could not be reached for comment. A spokeswoman in his office said she was reasonably certain Barry was not aware of the bill and probably could not comment on it until he had read it.

"But the mayor, of course, would oppose anything which would weaken the powers of the city government," press secretary Annette Samuels said. Samuels also said the bill apparently conflicts with a D.C. law that requires city employes to move into the District after they are hired.

City Council member David A. Clarke (D-Ward 1), chairman of the council's Judiciary Committee, said the move to reduce the commission's powers was made to "take advantage of an unfortunate situation regarding Mr. Borders to weaken one of the aspects of home rule which was not very strong in the first place."

Clarke also said he opposed allowing local judges to live outside the city. "I can understand his putting it in there, but it is certainly something no other state has," Clarke said.

Several D.C. officials said they were surprised that Mathias, long considered a supporter of home rule, introduced the bill. Mathias could not be reached for comment and his aides declined comment on the senator's reasons for introducing the legislation.

"I'm quite disappointed in the author of this bill," businessman John W. Hechinger, a member of the commission, said yesterday. "It's very unlike him."

An aide to Del. Walter E. Fauntroy (D-D.C.) said the congressman "was unalterably opposed to the bill." Fauntroy has introduced legislation in the House to give the mayor the right to name judges to the D.C. courts.