Fifty-seven percent of respondents also support legal possession of marijuana in small amounts, edging out 31 percent who opposed such a measure.
Support for a law allowing smoking marijuana with a prescription is bipartisan: While 93 percent of registered Democrats favor it, so do 82 percent of Republican voters.
Where they split, however, is on recreational use. Sixty-five percent of Democrats and 39 percent of Republicans support it, while 32 percent of Democrats and 55 percent of Republicans oppose.
Even if most of them support reformed marijuana laws, less than half of those polled admitted having smoked pot before.
"Medical marijuana is a no-brainer for New York State voters, and they also would follow Colorado in legalizing marijuana for fun," wrote Maurice Carroll, director of the Quinnipiac University Polling Institute, adding that a slim plurality — 41 percent — think legalization hurt Colorado's national reputation.
Across the country, 20 states and the District of Columbia allow some form of medical marijuana use. New York might join that list if Gov. Andrew Cuomo's own proposal passes through Albany.
The poll surveyed 1,488 New York State voters and has a margin of error of plus or minus 2.5 percentage points.