Though there is no evidence behind President-elect Donald Trump’s recent claim of “serious’’ voter fraud in New Hampshire, the state could see a handful of election law changes now that Republicans are in charge at the State House. Gov.-elect Chris Sununu wants to eliminate Election Day registration, while fellow Republicans in the legislature have long sought a 10- or 30-day residency requirement. They say the changes would give voters more confidence in New Hampshire’s election systems. ‘‘It’s simply about doing things the right way,’’ Sununu recently told WMUR-TV of his calls to eliminate same-day registration. Sununu was not immediately available for a comment to The Associated Press. The offices of both the Attorney General and Secretary of State say there aren’t enough complaints to back up any assertions of wide-scale voter fraud. Trump tweeted Sunday that the media is ignoring ‘‘serious fraud’’ in New Hampshire, Virginia and California, without providing evidence for his claims.