Why didn't Brian cooperate with the police?
Since Brian was innocent, and there was no real evidence to tie him to the murder, her could have just surrendered politely, given his statement, be investigated and then let go.
Then he could have investigated the case himself, perhaps helping the police more in the process, instead of choosing to fight the police while trying to catch the killer.
Did he think the killer was going to leave the country, or he was on an air tight schedule?
Why did he choose to make himself a suspect?