Smithsonian Secretary S. Dillon Ripley disclosed to a House Appropriations subcommittee yesterday that the institution's board of regents, headed by Chief Justice Warren E. Burger, will decide next month whether future regents' meetings should be open to the public.

Ripley's disclosure came after Rep. Sidney R. Yates (D-Ill.), chairman of the Appropriations Subcommittee on the Department of Interior and Related Agencies, and Rep. Ralph S. Regula (R-Ohio), a subcommittee member, suggested that the regents ought to open their meetings because they regularly make decisions involving federal money.

The Smithsonian has recently been criticized by the General Accounting Office, members of Congress and the press for its lack of accountability to Congress and the public for the more than $100 million a year it receives in federal appropriations.

The regents, who govern the Smithsonian, include the Chief Justice, the Vice President, six members of Congress and prominent private citizens from around the country. Their meetings, held three times a year, are traditionally closed to all but a few high-level Smithsonian officials.

The House Appropriations subcommittee concluded two days of hearings yesterday on the Smithsonian's request for $106.5 million in federal funds for the 1978 fiscal year.

Among other topics, Yates questioned Ripley about a recent story in The Federal Times that said that Ripley, a noted ornithologist, has birds belonging to the National Zoological Park at his private waterfowl preserve in Litchfield, Conn.

Ripley acknowledged that he does regularly trade birds and other animals with the zoo for breeding purposes. Dr. Theodore Reed, director of the zoo, and Ripley defended the practice but Yates said he thought this subjects Ripley to criticism and told the Smithsonian secretary tht his activities should be above reproach.

"I think there's a question of Caesar's wife," Yates told Ripley. Addressing himself to Reed, Yates said: "My reaction would be that if you're going to have outside breeders, then you ought to send them (the National Zoo's birds) to zoos other than Dr. Ripley's."