ALBANY — A new poll released on Wednesday seemed to give a lift to Gov. Andrew M. Cuomo as he quarrels with Mayor Bill de Blasio over the best way to pay for prekindergarten classes.

But the way the question was worded makes the results of the poll much less conclusive.

Mr. Cuomo wants the state to pay for an expansion of prekindergarten in school districts across the state. Mr. de Blasio, a fellow Democrat, has his own plan that is specific to New York City: He wants to raise taxes on high-earning city residents, with the extra money to go toward prekindergarten and after-school programs in the five boroughs. The tax increase requires state approval.

The poll, by Quinnipiac University, asked voters to choose between the two ideas. Forty-seven percent of voters statewide said they favored the governor’s plan, while 37 percent sided with the mayor’s. The margin of sampling error was plus or minus three percentage points.

Voters in New York City appeared split over the proposed tax increase: 49 percent sided with Mr. Cuomo and 40 percent with Mr. de Blasio, a difference that is statistically insignificant given the poll’s margin of error for the subgroup of city voters. Over all, the poll, conducted by telephone from Feb. 6 to 10, included 1,488 voters across the state.