President Donald J. Trump twice sought to talk on the phone with the Republican leader of Arizona’s most populous county last winter as the Trump campaign and its allies tried unsuccessfully to reverse Joseph R. Biden Jr.’s narrow victory in the state’s presidential contest, according to the Republican official and records obtained by The Arizona Republic, a Phoenix newspaper. But the leader, Clint Hickman, then the chairman of the Maricopa County Board of Supervisors, said in an interview on Friday that he let the calls — made in late December and early January — go to voice mail and did not return them. “I told people, ‘Please don’t have the president call me,’” he said. At the time, Mr. Hickman was being pressed by the state Republican Party chairwoman and Mr. Trump’s lawyer Rudolph W. Giuliani to investigate claims of fraud in the county’s election, which Mr. Biden had won by about 45,000 votes.