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A young marijuana plant is shown at a medical-marijuana dispensary in San Jose, Calif. New York Gov. Andrew Cuomo plans to allow limited access to medical marijuana for patients with qualifying conditions.

(David Paul Morris | Bloomberg News)

SYRACUSE, N.Y. -- Nearly 4 out of 5 New Yorkers favor using marijuana for medical uses, according to a poll out this morning from the Siena College Research Institute.

But how to legalize medical marijuana is a different matter. A third of voters favor a plan from Gov. Andrew Cuomo, which would use existing law to allow 20 hospitals to dispense the drug and oversee treatment.

More people (45 percent statewide and 47 percent Upstate) said Cuomo's medical marijuana plan doesn't go far enough. They favor legalization of medical marijuana more similar to laws passed in 20 other states, the poll found.

"New Yorkers, however, are not ready to see New York join Colorado and Washington and legalize the recreational use of marijuana," said Siena pollster Steve Greenberg.

Statewide, 43 percent of those polled said they supported full legalization of marijuana, with 53 percent opposed. That's little changed from last month's poll, according to Siena.

Siena surveyed 802 registered voters from Feb. 16 to 20 by phone. The poll has a margin of error of plus or minus 3.5 percentage points.

Contact Teri Weaver at tweaver@syracuse.com, 315-470-2274 or on Twitter at @TeriKWeaver.