City councilors in Quincy are considering passing new zoning restrictions, and officials in Randolph hope to have similar regulations drafted by Christmas. In Hanover, town officials are working with police to get a proposal ready by spring Town Meeting, and in Milton, the police chief is scheduled to discuss the issue with selectmen at their meeting Thursday.

Meanwhile, the police chief in Norwood says he wants to work with state health officials to establish detailed policies regarding enforcement of the new law. Officials in Abington, Avon, Braintree, Dedham, Halifax, and a number of other communities are also starting to take a closer look at their zoning rules to see what can be done.

“We are looking at doing something . . . so we have some control over what’s going to happen,” said Avon Town Administrator Michael McCue. 

The flurry of activity follows the convincing decision on Question 3, approved by 63 percent of Massachusetts voters. Slated to take effect Jan. 1, the measure will allow people with certain medical conditions to possess up to a 60-day supply of marijuana, and paves the way for 35 nonprofit “medical marijuana treatment centers” to open over the next year.

The law calls for there to be at least one, but not more than five, of these centers in each of the state’s 14 counties, and allows them to grow, process, transport, and sell marijuana to qualifying patients.

The potential of a “pot shop” opening in their midst has riled opponents of the measure and has put many city and town officials on guard. Local officials are anxiously waiting for the state Department of Public Health to release more details about how the new law will work.

The Massachusetts Municipal Association has asked the Legislature to delay implementation of the law, giving cities and towns more time to review and update their ordinances and zoning rules in preparation for what could be coming to their community.

“This is something that has been illegal forever in Massachusetts, up until this point,” said Geoffrey Beckwith, executive director of the Massachusetts Municipal Association. “Communities have never had an opportunity to discuss rules on where marijuana dispensaries should be located. Communities need to have time, and we hope that they are afforded that.”

In Randolph, where 58 percent of voters in town voted “yes” on Question 3, Councilor at Large James F. Burgess Jr. said he hopes the Town Council will consider some proposed regulations by Christmas that would limit where medical marijuana dispensaries can be located.

“If they opened by schools, public parks, we’d be very concerned,” said Burgess.

In Quincy, where 61 percent of voters approved the ballot question, Ward 4 Councilor Brian Palmucci has proposed an ordinance that would prohibit marijuana dispensaries from opening within 1,500 feet of a school, day-care center, or residential neighborhood. Palmucci said he based the language on regulations that are in place in Denver (medical marijuana has been legal in Colorado for more than a decade).

“My worst fear is . . . a corner convenience store will say, ‘Hey, I could make some money off of this,’ and clear half their shelves to sell marijuana,” said Palmucci. “It’s the kind of thing we don’t want in a residential neighborhood or a school.”

Palmucci said he wants “community standards in place, in writing, on day one” when the law takes effect. His proposal is being reviewed by the City Council’s Public Safety and Ordinance committees.

Palmucci said he’s already received phone calls from people interested in opening marijuana establishments in Quincy, as well as phone calls from “a half-dozen” municipalities asking for a copy of the ordinance he drafted.

“I just wanted to start the discussion and get something in place before the new law went live,” he said. “We just want to set some reasonable regulation of where these things can go.”

Palmucci hopes that the city will adopt the new ordinance and that it can serve as a model for other municipalities.

In many communities south of Boston, any local bylaw or zoning changes have to approved by Town Meeting.

Halifax Town Administrator Charlie Seelig said officials in his community are taking a closer look at its zoning rules.