NEW YORK (Reuters) - Forty-five per cent of New York state voters support natural gas drilling in the Marcellus Shale for the economic benefits versus 41 percent who oppose it because of its environmental impact, a poll said on Wednesday.

Support for a new tax on drilling companies fell to 51 percent from 59 percent in August, the Quinnipiac University poll said.

Quinnipiac began measuring public sentiment on gas drilling a month ago as New York state considers whether to open its share of the Marcellus Shale to hydraulic fracturing, or "fracking," a method that environmentalists oppose.

The 45-41 margin in favor of drilling showed a minor decline in support of 47-42 from a month earlier, a difference within the margin of error of plus or minus 3.1 percentage points. This month's poll surveyed 1,016 registered voters from September 13-18.

Republicans supported drilling by a 69-20 margin while Democrats opposed it 52-35.

Fifty-one percent of those polled support a new tax on drilling companies versus 36 who oppose a new tax. A month ago, 59 percent of those responding supported the tax versus 29 percent in opposition.

(Reporting by Daniel Trotta; editing by Jim Marshall)