District of Columbia residents are complaining in growing numbers of the City Council that many city government information telephone numbers - especially those for tax and motor vehicle information - are constantly busy and provide little service.

Alan Grip, special assistant to Council Chairman Sterling Tucker, said he called the number for real estate tax information in the Department of Finance and Revenue at least 30 times in a two-day period last week. "I got a busy signal every time," he said. Other council aides reported similar difficulties and complaints.

T. J. (Dutch) Behrens, chief of the city government's telephone management division, acknowledges that the phones "sometimes get jammed up, especially around tax time (April 15)."

Contrary to the popular belief that information numbers have only one line answered by a single employe, he said, most information numbers have a "rotary" capability that automatically diverts calls on busy lines to other lines.

The real estate tax information number, 629-3135, for example, has a four-line rotary, Behrens said, and the personal income tax information number, 629-3324, has a six-line rotary. Motor vehicle services information in the Department of Transportation, he said, has two 10-line rotaries.

Even so, "You'll get a busy signal during busy times . . . There are only so many (employes) available. We can put in only as much (telephone) service as we have people, he said.