A bill to force skating rinks to close at 11 p.m. and to make operators liable for the disorderly conduct of patrons on their property was filed yesterday before the Prince George's County Council after a weekend fracas near a Marlow Heights rink in which three teen-agers were injured.

The council voted unanimously to send a letter to County Executive Parris Glendening asking him to provide "whatever assistance" the police department might need to control such situations.

Complaints about the rink are not new. Yesterday, council members received a two-month-old staff memorandum outlining some problems there.

The memo from legislative officer Robert E. Payne to council administrator Samuel E. Wynkoop reported that "large numbers of skaters leaving the facility" have caused "disruption of the neighborhood, alleged widespread drug use, cutting the gas pump hoses of an adjustment service station, pilferage of convenience stores in the area, and disportionate concentration of available police in the area."

In the latest incident, one teen-ager was shot, another stabbed and a third hit by a car early Saturday when more than 2,000 young people turned into a mob after leaving the Crystal Skate rink on Branch Avenue.

It took more than 30 officers to quell the disturbance after the rink's 3 a.m. closing.

"For teen-agers to be out on the road at 3 a.m. is unacceptable," said council member Sue V. Mills, who proposed the legislation. "They should be at home. Mob psychology takes over, just by the sheer numbers."

Mills' bill, which was referred to the council's Fiscal and Planning Committee for study, would require the four ice and roller skating rinks in the county to obtain annual $150 licenses. Under the bill's provisions, the county could suspend the license if there is a disturbance. Violations would be punishable with fines of from $200 to $1,000.

Council Vice Chairwoman Hilda Pemberton, whose district includes Crystal Skate, noted that the rink owner had extended his hours at the request of neighboring merchants who closed earlier and wanted their patrons out of the area "before the kids leave the rink."

The rink owner, Daniel McDermott, has agreed to meet with county officials and to provide more security.

The council letter to Glendening, signed by Chairman William B. Amonett, noted, "The violence that erupted last weekend . . . was not an isolated incident . . . . Council members have been personally involved with this problem for some time and now feel the situation is totally out of control."

Tim Ayers, a spokesman for Glendening, said that the county office of law also will investigate other means of regulating the rinks.

In other action, the council voted to approve a request by the nonprofit corporation that runs the county's three public hospitals to delay more than $2.6 million in rent payments to the county until Dec. 31.