City Council member John A. Wilson (D-Ward 2), responding to complaints about the abrupt closing of the Anthony Bowen branch YMCA, has scheduled a public hearing to examine the tax-exempt status of property owned by the YMCA of Metropolitan Washington.

"Basically, we will focus on why we are giving tax-exempt status if the organization is not serving the community that it is supposed to serve," said Wilson, chairman of the council's finance and revenue committee.

The hearing is scheduled for 6 p.m. April 7 in Room 500 of the District Building.

Council member David A. Clarke (D-Ward 1), who represents the Shaw community where the Bowen Y is located, asked for the hearings after the YMCA board of directors voted 19 to 1 to close Bowen Feb. 23 because some board members said it was unsafe.

Clarke said he felt the tax exemption was valid only as long as the YMCA operated Bowen as part of its programs and would not apply to any land or buildings owned by the Y organization but not used for its programs.

The closing stirred a strong community response, including charges that the YMCA was not fulfilling its commitment to the Bowen Y, which served the middle-income and poorer neighborhoods of Shaw.

The Bowen Y, constructed in 1912, was named in honor of a freed slave in Washington who in 1853 established the first YMCA for blacks.

The YMCA organization, which has a $6 million annual budget, employs about 700 persons, operates 11 branches and serves about 200,000 persons in a broad range of programs.

The YMCA is exempt from real estate and various business taxes in the District. The real estate exemption was mandated by Congress in the 1890s. Wilson said he was unsure of the legal problems the city might have if it decided to revoke the exemptions or attempted to tax part of its holdings.

"We would not like to remove anybody's tax exemption," Wilson said. "Our purpose is to stress to the YMCA the purpose of its tax exemption, and find out whether they are interested in service to the city."Cable TV Vote Delayed

Council Chairman Arrington Dixon announced this week that the Council's cable televison bill, originally scheduled for a final vote next Tuesday, has been put off until April 6.

Dixon said the council, which in a marathon session gave preliminary approval to the cable bill about 2 a.m. March 10, had technically not met the deadline of approving the legislation two weeks before taking a final vote on the issue. Dixon said the issue could not come up again until the council's next regularly scheduled legislative session.

The delay gives Dixon's staff time to assimilate more than 40 amendments that were offered to the bill which would set up a 28-member commission to guide the city in selecting potential cable franchise operators.