As the state begins vetting applications for medical marijuana dispensaries, the Boston Public Health Commission is asking for authority to permit and inspect the shops that would open in the city.

Twenty-one of the 181 applications collected last week by the state Department of Public Health proposed a dispensary in Suffolk County, and most of those are likely to be in Boston. Applicants must first clear a screening of their criminal history and finances. State officials will begin a more detailed review of proposed locations and operations next month.

Those sited within the city limits also should be subject to a local review, said Dr. Barbara Ferrer, the commission’s executive director. The commission plans to ask the Boston Board of Health, which creates its regulation, to grant it oversight authority.

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“We need to support patient access as well as ensure that neighborhood and public health interests are met, and we believe that an additional local regulation can help accomplish that balance,” she said in a press release.

The dispensaries must follow a seed-to-sale model, growing the large majority of the marijuana products they sell to customers, who are required to have doctor approvals to use the drug and must register with the state. Under the medical marijuana law passed by voters in November, no more than five dispensaries may be licensed in each county, for a total statewide of 35.

The city could get involved in aspects not covered by the state regulations, including the content of educational material distributed to patients, the nature of signs advertising the shops, hours of operation, and security requirements, the commission’s statement said.

State rules require dispensaries to be located at least 500 feet from places that serve children, including schools and community centers. The city has already changed its zoning rules to prohibit them from residential areas and to require a hearing before the zoning board of appeals.