Gov. Harry Hughes yesterday injected himself into efforts of Montgomery County legislators to strip the Burning Tree Club of its $152,000 annual property tax exemption.

Hughes telephoned Sen. Thomas L. Bromwell (D-Baltimore County) in the Senate Finance Committee and asked him to vote for legislation that would eliminate the tax break, granted to the all-male Bethesda golf club for providing open space, because it discriminates against women. Bromwell has said he has problems with the legislation because it also would strip groups such as the Elks, Moose and Masons, which are very strong in his district, of their tax exemptions.

The measure, which passed the House of Delegates last week, was scheduled to be voted on by the committee yesterday but delaying tactics by opponents postponed the vote for at least a day.

The committee is split 4-4 on the bill, with Bromwell the swing vote. Five votes are needed to give the legislation a favorable report. If the committee approves the measure, Sen. Stewart Bainum Jr. (D-Montgomery), the chief sponsor, said he thinks he can just get the 24 votes needed to pass the full Senate.

If the vote remains 4-4, committee chairman Rosalie S. Abrams (D-Baltimore), who favors the bill, is likely to bring the bill to the floor anyway. But without the support of a majority of the committee, some members who now are committed to vote for it would have an excuse to change their vote.

A series of amendments offered by Sen. Dennis F. Rasmussen (D-Baltimore County), an opponent, delayed a vote yesterday. With the session ending next Monday, approval of any amendment would likely kill the legislation because it would require the bill to go back to the House for concurrence. The four favorable votes are enough to stop the amendments.