A Long Island research group is urging local governments to consider allowing more rental apartments in private homes, to help cash-strapped homeowners and provide more housing for renters.

In a report released Saturday, the Long Island Index outlines the vast differences in the ways Long Island’s towns, cities and villages deal with so-called accessory apartments, or small units within owner-occupied homes.

The approaches range from fairly accepting — as in the Town of Babylon, where homeowners can get permits to rent out apartments if they meet certain conditions — to strict, as in the Town of North Hempstead, where such units can only be occupied by the homeowner’s parent or child.

Long Island has a patchwork of rules for accessory apartments, which vary so widely that many homeowners fear getting penalized, so they don’t even try to create apartments, even if they want to and might be allowed, said Nancy Rauch Douzinas, publisher of the Index. The Index is a project of the Garden City-based Rauch Foundation, which funds research on housing, planning and the environment.

For those struggling to afford life on Long Island, creating more rental apartments in private homes “could be a big, immediate win,” said Douzinas, who is also president of the Rauch Foundation. She said she’d ask local officials: “Look around you. Do you want more young people living here? Do you want people who are moving away to have another option?”

Officials say local rules limiting apartments are intended to respond to residents’ concerns about safety, quality of life, neighborhood character and property values.

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In Suffolk County towns such as Babylon, Brookhaven, Huntington and Islip, homeowners can get permits to rent out apartments if they meet requirements for fire safety, minimum or maximum apartment size, utilities, entrances and parking, the Index reported. By contrast, Nassau County towns tend to take a stricter approach, with the cities of Glen Cove and Long Beach not allowing accessory apartments at all, and the towns of Hempstead, North Hempstead and Oyster Bay setting conditions such as allowing them only for immediate family members, or only for elderly homeowners.

A 2016 study by the National Center for Suburban Studies at Hofstra University estimated that Long Island has 14,500 to 16,000 legal accessory apartments, making up about 7 percent of the Island’s total rental stock. According to the Index, local officials estimate there are 90,000 to 100,000 illegal apartments on the Island.

Babylon was one of the first towns to start issuing permits for accessory apartments, in the late 1970s.

“We’ve had a great experience with it,” said Town Supervisor Rich Schaffer. The permitting process was initially meant to let young adults live in separate units within their parents’ homes, he said, but “it now gives some of the seniors the ability to stay on their own while getting some income that helps pay the property taxes and other costs associated with the house.”

One of the most important rules is that the home must be owner-occupied, he said. “It guarantees that you can hold somebody accountable,” he said.

By contrast, in North Hempstead town officials passed a measure in 2008 allowing certain accessory apartments — but quickly threw it out after an outcry from local residents.

“It was just a matter of residents not wanting strangers in the neighborhood, more garbage, more children in schools and cars on the streets,” among other concerns, said John Niewender, town building commissioner. North Hempstead, he said, is already “a very concentrated area.”

To be sure, in certain areas “there remain concerns about the ways accessory housing might change the character of some suburban communities,” said Christopher Niedt, academic director of the National Center for Suburban Studies. However, he said, “the complexity of the regulations and the fact that they’re not uniform across the region discourages people from legalizing apartments that they do have.”

Legal accessory apartments are a boon for young homeowners as well as seniors, said Jo Ann Boettcher, president of the Lindenhurst Chamber of Commerce and an agent with Douglas Elliman Real Estate in Babylon.

“When it’s a young family it helps one partner to be a stay-at-home parent,” she said. In some cases, the rental income funds much-needed renovations, or allows first-time home buyers to afford a house, she said.

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Jeannie DeMaio, 56, said she was relieved to find an apartment in a private home after her first marriage ended in the early 1990s.

The two-bedroom apartment cost $700 a month — about half the price of a rental in a multifamily building — which allowed her to make car payments, travel and enjoy her life, said DeMaio, who now works as a grants administrator and office manager at the Long Island Community Foundation, which funded the National Center for Suburban Studies’ research on accessory housing.

“I was able to take care of myself without going to anybody for help,” said DeMaio, who has since remarried and now lives in Bellmore. “It was a win-win . . . I was helping them pay their taxes, and they were giving me a safe place to live.”

Since that time, she said, “the rents have gone up significantly, but salaries have not changed that much. For young people today, I don’t know how they would make ends meet.”