SEATTLE — Gov. Jay Inslee wants the state Liquor Control Board to figure out how to stop the spread of bars that allow patrons to consume marijuana on site.

Voters last fall legalized marijuana for adults over 21, but Initiative 502 prohibits the public use of marijuana, which typically would include bars and restaurants.

While most bars are steering clear of allowing pot use until officials come up with rules, a few have been testing the boundaries, The Associated Press reported last week. The AP wrote about two venues in Washington state —Frankie’s Sports Bar and Grill in Olympia and Stonegate in Tacoma — that allow pot use.

That prompted concern from the governor.

“We think the board needs to give this a very hard look,” Inslee spokesman David Postman told The Seattle Times in a story published Sunday. “We will implement the will of the voters and create a well-regulated industry. Washingtonians did not vote for a wide-open policy.”

Liquor Board chairwoman Sharon Foster said she expects the board to try to come up with a rule to deal with the situation.

“We’re proceeding at next week’s board meeting with proposed rule-making to deal with the potential issue,” Foster said Friday.

“Once people are aware this is a business model they’re going to be popping up all over the place,” board enforcement chief Justin Nordhorn warned members in a meeting last week.

He noted that there’s “a loophole in the law that doesn’t allow the board to hold licensees accountable” for such activity.

Washington’s law bans pot distribution by anyone but a licensed seller — and no such licenses will be issued until the end of the year at the earliest. There’s also a statewide smoking ban that prohibits smoking where people work.

Frankie’s allows members of its private smoking room to use tobacco or marijuana. To evade the smoking ban, there’s no smoking allowed at Stonegate — only “vaporizing,” a method that involves heating the marijuana without burning it.

State officials are concerned that marijuana can compound alcohol’s intoxicating effects.

According to the Times, Nordhorn said the state’s new pot law bans use in public view, but doesn’t define public view.

“If you’ve got a private room, and patrons pay a fee to be a quasi-member and they’re not in public view, you run into enforcement problems because they’re not openly consuming in public,” he said.

If patrons are ingesting their own personal supplies, the only enforcement action under the state law is to issue civil infractions, which come with $103 fines, against customers for public use, Nordhorn told The Times.

Board enforcement officers have not yet fined pot-using patrons, because they are waiting for the board to write rules for the new law, he added.

That is more labor- intensive than citing bar owners for violations. It also raises questions about the public’s understanding of the law, Nordhorn said, and whether an education campaign would be a more appropriate starting point than fines.

Frankie Schnarrs told The Times he has no intention of changing his bar’s policy. His pot-patrons are well-behaved, he said, and most are medical-marijuana patients.

“What the hell is the difference,” he said, “if somebody smokes in the parking lot or inside?”