New York is still grappling with the redistricting required as a result of the 2010 census. The State Legislature has now approved proposed new districts for the Senate and Assembly, and Gov. Andrew M. Cuomo has signed them in exchange for the Legislature's pledge to seek to amend the State Constitution to create a bipartisan panel that would oversee redistricting after the 2020 census. The Legislature gave up its efforts to reach an agreement on a new Congressional district map and has left that task to the federal courts. Late Wednesday night and early Thursday morning, the Legislature voted to approve the redistricting compromise negotiated with Mr. Cuomo. As part of the agreement, lawmakers approved three redistricting measures: the new maps for the Senate and Assembly, the proposed constitutional amendment that would create a bipartisan redistricting commission after the 2020 census, and a law intended as a backup of sorts in case the Legislature does not approve the amendment a second time, as is required by the State Constitution. Mr. Cuomo signed the Senate and Assembly maps into law on Thursday. But Senate Democrats, who boycotted their chamber's vote on the maps, filed a lawsuit on Thursday in State Supreme Court in Manhattan challenging the addition of a 63rd seat in the Senate's plan. An earlier lawsuit on the subject was dismissed because the Senate redistricting plan had not yet been enacted. On the Congressional front, a panel of federal judges held a public hearing on Thursday in Brooklyn to consider objections to the map proposed by a federal magistrate judge, Roanne L. Mann. Meanwhile, the Justice Department will review the new Senate and Assembly maps to determine whether they disenfranchise minority voters.