The Rockland City Council has asked the administration to consider changes in hours of operation at the library in order to keep it open on Sunday afternoons.

The council reviewed the proposed 2010-2011 library budget May 17. The budget proposed by City Manager Rosemary Kulow calls for eliminating the 1 to 5 p.m. Sunday hours to save $8,500.

Library Director Amy Levine said the Rockland library is heavily used. Her budget message notes that state library statistics list Rockland as the sixth busiest library in Maine with 203,000 people visiting it last year.

Councilor Tom Molloy questioned those numbers. Levine said there is a device that records when people come through the doors. Molloy said this includes teens who go in and out the door repeatedly.

Levine maintained that the library is heavily used with the state listing Rockland as the fifth highest in terms of Internet use.

The library budget is proposed at $555,554, up $1,420.

“That’s a lot of money,” Molloy said.

He also said the library serves people from outside Rockland who do not pay property taxes to support the department’s operations.

Mayor Deborah McNeil asked if the administration could return with a proposal that would keep the library open on Sunday afternoons. The library has been open on Sundays from 1 to 5 p.m. since 2007.

One suggestion by the mayor was to eliminate Monday evening hours and open an hour later on Tuesday and Thursday mornings. The library remains open until 9 p.m. on Mondays and opens at 9 a.m. every day except Sundays.

No decision was made and the administration will come back with a revised plan.

Another budget review session is scheduled for Wednesday, May 19 at 6:30 p.m. at city hall, with departments starting with the letters H through W to be scrutinized.