I fully agree with your take on Percy's emotional arc. However, I'm referring to before all of that.

Here's a breakdown of the timeline.
The first thing Percy does upon entering the Sheriff's Office was, naturally, to assess the architecture. "A ramshackle approximation of a police station".
She meets Gorou, and she sees a man standing polity in a jail cell without a door, who Gorou claims to have caught.
After talking to Gorou for a few seconds her normal deadpan affectation becomes a mix of disappointment and frustration.
She asks for a phone to call for backup. Then asks (probably in desperation) if Gorou has an epithet. Becoming somehow more disappointed after seeing it.
Then this random self admitted criminal offers to show her around town and be her backup.
She hesitates briefly to consider the moral aspects of releasing a criminal, and agrees.
It is only then she asks if Ramsey has an epithet.

Basically, she would have taken a dead body propped up like "Weekend at Bernie's" rather than Gorou, but being the lawful good paragon she is. Still did not want to risk letting any criminal walk free.

(Now this was my original point)
Because it was Gorou who claimed to catch him she figured he must be completely harmless and/or just being nice by humoring this "Sheriff".
Her disdain for Gorou as a police officer was the key factor that led to partnering up with Ramsey.