The Board of Selectmen considered naming a new town administrator Tuesday, but decided to wait until more background checks could be done on three of the four finalists, said William Heitin, chairman of the selectmen, in an interview. Making the decision is important and is “probably one of the hardest things I’ve done for the community,” he said. Checks will be done on Timothy King, assistant town administrator in Wellfleet; Grady Miller, former town manager in Narragansett, R.I.; and Frederic Turkington, former town administrator in Wayland. The fourth finalist is Michael McCue, town administrator in Avon. Richard Powell, who resigned from the Board of Selectmen to apply for the position, was not among the finalists selected by a search committee. Heitin said Powell was qualified but that other candidates had especially strong qualifications. The board could vote on the new administrator Tuesday if the research is complete, he said.