Yeah, i agree it was a stupid move by Heyward. I can't recall, but was Columbo closing in or Heyward just getting paranoid? I know Columbo asked a sergeant to let him know if Heyward goes to his office alone so he was sniffing something out.
His Alibi really started falling apart when he was filming that scene at his own home. When Colombo confronted him about the gas station where the phone was. The fact that the gas station closed.