Sixty-seven-year-old Gregory Hopkins used to be a borough councilman in Bridgewater. He is charged in the death of a woman with whom he was having an affair.
Twenty-three-year-old Catherine Walsh was found strangled and bound in her Monaca apartment in September 1979.
Hopkins was charged in 2012 after new DNA evidence linked him to case.
Lawyers for both sides finished their closing arguments Thursday morning in Beaver County Court. Deliberations began after closings and will resume Friday.
Hopkins has testified that he hadn't been to Walsh's apartment for a few weeks and wasn't there the night she died.