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Bloomberg reports that lawmakers have settled on language in the bill, which is expected to mirror laws from neighbouring states - where the legal age to buy cannabis is 21.
State Senate Finance Committee Chair Liz Krueger told the outlet yesterday: "It is my understanding that the three-way agreement has been reached and that bill drafting is in the process of finishing a bill that we all have said we support."
The deal would legalise cannabis for adults aged 21 and over, with Krueger explaining it includes 13 percent sales tax - nine percent of which would go to the state, and four percent to the localities.
According to Bloomberg, distributors would collect an excise tax of as much as three cents per milligram of THC (the active ingredient in cannabis), with a 'sliding scale based on the type of product and its potency'.
Krueger added that no changes would be made to the taxes already imposed on marijuana sold for medical purposes.
The Wall Street Journal reports that the deal would allow residents of the state to buy and possess up to three ounces of marijuana, and even let them grow plants for personal use.
So far, 14 US states and three territories have legalised recreational marijuana, according to the National Conference of State Legislatures.
New York Governor Andrew Cuomo revised the New York legalisation proposal last month, following a long-running dispute with state lawmakers arguing it did not do enough to address the effect marijuana prohibition takes on minorities.
He has since vowed to set aside $100 million (£73,000) for a social equity fund, which is designed to help communities hit by marijuana laws through job placement programmes and treatments.
In a news conference this week, Cuomo said he was making marijuana legalisation a top priority in budget negotiations with officials.
He said: "This year we have to get it done, and getting it done by the time the budget is passed is essential.
"Cannabis is not just social equity, it's also revenue for the state."
Cuomo also said that marijuana should have been legalised 'years ago', adding: "We've been trying to legalize cannabis for three years. I've failed every year.
"We're close. Close three times before. If we were playing horseshoes, we would be in good shape. But this is not horseshoes. You either get it done and sign a bill, or you don't."
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