LITTLE ROCK — The Arkansas Medical Marijuana Commission on Tuesday set the scoring system it will use to evaluate applications for licenses to operate medical-marijuana dispensaries and cultivation centers in the state.

The five-member panel plans to publish notices June 20 that it will begin accepting applications for licenses on June 30. The application period will last 90 days. The commission does not have a deadline for deciding whether to approve or deny applications, a process that will not begin until after after the application period ends.

In November, Arkansas voters approved a constitutional amendment to legalize medicinal use of marijuana, with a doctor’s recommendation, by people with certain health conditions. The amendment initially set a June 1 deadline for the state to begin accepting applications for dispensaries and cultivation centers, but the state Legislature voted earlier this year to move the deadline to July 1.

The amendment allows the commission to issue licenses to up to 40 dispensaries and eight cultivation centers, but the panel has chosen to grant up to 32 dispensary licenses and up to five licenses for cultivation centers, at least initially. The commission could grant more licenses if it sees a need, within the limits set in the amendment.

The commission plans to grant up to four dispensary licenses in each of eight geographical zones. There are no restrictions on where cultivation centers can be.

Joel DiPippa, an attorney for the state Department of Finance and Administration, told the commissioners Tuesday they should be prepared to explain the scores they give to the applications.

“I’m a lawyer. I’m conservative. I’m expecting, you know, the possibility of lawsuits,” he said.

Commissioner Travis Story of Fayetteville, also a lawyer, said after the meeting he agrees there is good chance of legal challenges to the commission’s decisions.

“There’s a lot of money at stake in this,” he said. “It wouldn’t surprise me if somebody resorts to litigation in one form another. I’m hoping that we don’t have that.”

The commission was created under the medical-marijuana amendment. It includes one member appointed by the governor, two appointed by the House speaker and two appointed by the Senate president pro tem.