Hospitals seeking a foothold in medical marijuana are generally academic medical centers that could use access to the drug to research its impact on diseases like Alzheimer’s, epilepsy and cancer. Licensure could also ensure that their patients would have access to the drug, since insurance companies do not cover medical marijuana.

GNYHA Ventures, the business arm of the Greater New York Hospital Association, a hospital trade group, is also part of an application, according to a spokeswoman for the group. The association did not release further details on Friday.

Two other major academic medical centers, the University of Rochester Medical Center and Mount Sinai Health System in Manhattan, said they had been in talks with one or more companies that had applied for a license and would work with them if they were chosen by the state. But the medical centers said they were not applying themselves for medical marijuana licenses.

Peter Robinson, chief operating officer of the University of Rochester Medical Center, said that the medical center had entered into talks, not contracts, with any companies it supported, but that the center was “positively encouraged” it would have “relationships going forward if they get one of the licenses.” He said Rochester Medical Center would not have an on-site dispensary, because of difficulties with having for-profit activity inside of a nonprofit medical center.

The Health Department expects to choose up to five producers within the next month or so, officials said. Those five producers would each be able to run up to four medical marijuana dispensaries in various parts of the state.