Support for returning New Orleans public schools to local control outweighed opposition to the idea in a Tulane University poll released Monday, just as state lawmakers are considering different bills that would do just that.

Overall, 51 percent of the New Orleans residents polled said they favor some kind of return of all schools to the Orleans Parish School Board, with 38 percent saying the schools should return by 2018 and 13 percent saying the transition should take place later.

That compares with 32 percent who said they favor the status quo, with most schools under a state agency; 17 percent were unsure or declined to answer.

The poll, commissioned by Tulane’s Cowen Institute for Public Education Initiatives, had a margin of error of 4 percentage points.

A bill introduced by Sen. Karen Carter Peterson, D-New Orleans, would bring all 52 schools now under the state-run Recovery School District back under the OPSB by 2019 . The RSD took over most of the city’s campuses shortly after Hurricane Katrina.

Another bill, by Rep. Joseph Bouie, D-New Orleans, would immediately bring back any school no longer deemed “failing” by the state.

Fans of the independent charter schools that have proliferated under the state’s watch — if they support the return at all — tend to favor Peterson’s bill. It says explicitly that the OPSB won’t be able to interfere with day-to-day management of schools that return. Critics of the RSD and the charter movement tend to think those provisions would place needless restraints on the locally elected board.

Either way, more poll respondents than not said they think the School Board is capable of managing all of the city’s schools: 41 percent to 35 percent.

In fact, more respondents said the OPSB is “effectively managing” the charter schools that fall under its purview than those who said the RSD is, although the difference was within the margin of error: 42 percent for the board compared with 40 percent for the RSD.

At the same time, 63 percent said schools should have the option of returning to state oversight if they aren’t satisfied with board control, an option that’s not provided for in either of the bills .

Overall, a large majority — 63 percent — said charter schools have improved public education in New Orleans, although racial disparities persist. Among white respondents, 72 percent said charters have improved education in the city, while only 57 percent of black respondents did.

The same split shows up in opinions on the return to local control. Only 32 percent of white residents favor returning the schools by 2018, while 43 percent of black residents do.