Less than a month after a new state law went into effect decriminalizing the possession of small amounts of marijuana, law enforcement leaders, both on Vineyard and around the commonwealth, are crying foul.

And already legislation has been proposed to toughen the statute.

The new state law makes it a civil instead of a criminal offense to possess an ounce of marijuana or less; there is a $100 fine for infractions. The law, which went into effect Jan. 2, was approved by 65 per cent of Massachusetts voters in a ballot initiative in November. And since then it has drawn criticism from the state attorney general, district attorneys and police associations.

Island police say the new law has created enforcement problems and legal questions for both officers and the court system.

West Tisbury police chief Beth Toomey said the law compels police to issue a citation if they find someone with less than an ounce of pot, when previously officers had more discretion to confiscate the substance and let the offender off with a warning.

Chief Toomey said the law creates a gray area when it comes to enforcement, because a person caught with less than an ounce of pot can refuse to identify himself to police. She said the law may also force police to send confiscated marijuana to the state for testing, consuming manpower and funding.

“We are a small police department. I don’t see this creating less work for officers; I see it potentially creating a lot more,” Chief Toomey said, adding: “What if everyone appeals the [civil infraction]? The scary thing is we won’t even know the implications until the summer. I’m worried people will come here and think it’s okay to smoke marijuana, when that simply is not true.”

Edgartown police chief Paul Condlin said his department is not equipped to issue proper citations for marijuana use. Chief Condlin said his department will enforce the new law, but he agreed it needs some tweaking.

“I don’t think the people who wrote it really thought about the repercussions. This needs a second look,” he said.

Tisbury police chief John Cashin agreed.

“This has become not so much an argument about decriminalization, but about the practical application of a law. People frequently misinterpret decriminalization for legality, and in speaking with people I get the sense they think it’s perfectly fine to have [less than an ounce] of marijuana, when it’s not . . . I envision this bringing up a number of issues about probable cause and search. “But we are an executive branch of law enforcement, not the judicial. We will enforce it.”

The Massachusetts Chiefs of Police Association last month filed corrective legislation to clear up some of the legal questions. A. Wayne Sampson, executive director of the statewide police agency, told the Gazette this week his group is not trying to circumvent the will of the voters.

“We are trying to correct some of the administrative deficiencies of this law . . . everyone is talking about the percentage of [the November] vote or how the police are out to violate the people’s rights. That is not the case. We are looking to fix the law so it does not create additional problems for our officers and our courts,” he said.

Mr. Sampson said the law poses a number of problems for police and courts, including the question of identification. “Somebody can tell police their name is Mickey Mouse and walk away; there is really nothing officers can do,” he said.

The law also contains language about levels of THC in a controlled substance, making it legal for someone to possess certain amounts of hashish, Mr. Sampson said. It also raises questions about drug testing requirements for certain public jobs.

“I can with say with certainty that people did not know they were voting to legalize hashish. And I am positive they didn’t know they were voting for something that could prevent someone applying for a job driving an ambulance or working for the MBTA from being tested for marijuana use,” Mr. Sampson said.

Ironically, the law as written could also make it easier for someone to gather information about a person’s record on marijuana possession, he said. Criminal offenses for marijuana possession were previously covered by CORI laws, which restrict public access to criminal records. But information on civil infractions is readily available through most town clerks or police departments, Mr. Sampson said.

More than one piece of legislation has been filed to amend the statute. State Rep. Cleon Turner, a Democrat from Dennis, has proposed an amendment making failure to pay three marijuana citations in a 12-month period a criminal offense.

Mr. Turner is also proposing a state law to give schools, employers and managers of public buildings the right to ban marijuana on their grounds.

Vineyard schools superintendent Dr. James H. Weiss said this week that the statute does not affect school policy. “We treat marijuana offenses now the exact same way we did prior to [Jan. 2]. Nothing has changed,” he said.

The state attorney general is also circulating a draft bylaw that would make using marijuana in public an arrestable offense with a fine of $300.

Cape and Islands district attorney Michael O’Keefe is among those who feel the statute needs revising. After the ballot question was approved in November, Mr. O’Keefe sent a letter to Gov. Deval Patrick outlining his concerns.

But Allen F. St. Pierre, executive director of NORML, a national nonprofit group that backs marijuana law reform, said all the criticism is simply sour grapes.

“There is this idea someone could walk down the Mass Pike smoking a marijuana cigarette, and if an officer stopped them and asked them for identification, they could just blow pot smoke in their face and keep walking. It’s almost comical,” he said, adding: “If the police ask someone for identification and they refuse, the officer can do a number of things . . . for starters he can arrest [that person] for failure to cooperate.”

Massachusetts is the 13th state to decriminalize smaller amounts of marijuana, and the first to do so through a public ballot vote.

“What is happening in Massachusetts is unprecedented,” Mr. St. Pierre said, concluding:

“I believe Massachusetts will fully join the ranks of other states that have made a logical and beneficial change for their citizens.”