The state Department of Public Health Friday released the list of the first applicants approved for a registered medical marijuana dispensary — with none in Dukes County, at least yet.

The state has given 20 applicants provisional approval for dispensary licenses. Two are in Barnstable County, one in Mashpee and one in Dennis, two in Plymouth County, one in Plymouth and one in Brockton.

Four counties are so far without a selected dispensary: Berkshire, Franklin, Dukes and Nantucket. The state said it is inviting eight applicants who were not approved for their suggested locations to reapply in those four counties.

A state law approved by voters in 2012 allows up to 35 nonprofit, registered marijuana dispensaries. There must be at least one but no more than five dispensaries in each county.

In a media conference call last Friday, state marijuana program director Karen van Unen said the 20 approved applicants went through a rigorous application process and still have several steps to complete before opening, including a final state public health inspection. She said most of the applicants have said they would be ready to open to patients this summer.

The DPH said Friday that it would continue to seek qualified dispensaries for the four counties without approved dispensaries, beginning with inviting the short list of applicants to reapply. Ms. van Unen said the state aimed to make decisions for those counties by early June.

“Without going into the specifics of each application, it was very important to us to make sure we have dispensaries in those counties and we weren’t prepared to settle for anything less than a highly qualified applicant,” Ms. van Unen said.

Four applicants from the Vineyard had made it to the final application phase to operate a registered medical marijuana dispensary, two with proposed dispensaries in West Tisbury and two in Vineyard Haven. All four were listed by the state as applicants who were not selected at this time.

Ms. van Unen said the applicants who were not selected will have an opportunity for a debriefing. She said they will not be able to participate in the next selection process for the four counties without dispensaries.

According to the state, dispensaries were selected based on the quality of the applications, with an expert review giving each applicant a score on a scale from zero to 163 points. The department also looked at geographic diversity, local support, meeting patient needs and public safety. A registered marijuana dispensary selection committee selected the locations, and Ms. van Unen did the final sign-off for the locations.

The four applicants from Dukes County were Susan Sanford of West Tisbury, doing business as Greenleaf MV Compassionate Care; Geoffrey Rose of West Tisbury, doing business as Patient Centric of Martha’s Vineyard Ltd.; Susan Wysocki, doing business as Kingsbury Group Inc.; and Michael Peters of Tisbury, doing business as MV Greencross Inc.

Patient Centric received a score of 125 and Greenleaf MV received a score of 118. MV Greencross got a score of 91, and the Kingsbury Group received a 65.

Mr. Rose, who also runs Our Island Club, told the Gazette he is still hopeful that he can open a dispensary on the Island, pointing out that Patient Centric of Martha’s Vineyard had the highest score on Vineyard.

“If nobody steps forward I’m hoping that the Department of Public Health will then award [the license] to the licensed applicant that had the highest score in the county,” he said.

In an emailed statement, Ms. Sanford said: “As part of a collaborative team effort in the application process, I feel I gave my best effort and earned the trust and respect of the Island community. The entire process has been enlightening and I look forward to continued involvement in facilitating a medical marijuana program on Martha’s Vineyard that provides our community and patients with the best care possible.” She is the owner of Vineyard Complementary Medicine in West Tisbury.

Since medical marijuana was approved by voters in 2012, Island towns have grappled with zoning bylaws and where to locate a dispensary on the Island. In recent months, Oak Bluffs and West Tisbury have adopted zoning bylaws for where dispensaries could be located.