Cheryl is not the first cop character I've had who wasn't allowed to carry a gun.
Back in 2005, I did what's known as a "24 hour comic", which is a sort of marathon for cartoonists - you have to create a 24 page comic in 24 hours. Part of the challenge is that you can't go into it with an idea: you have to hammer out the script in the time allotted.
The comic I made was called Sight. The main character was a detective named Matt Sutherland, who was restricted by court order from carrying a firearm.
...Well, okay, no, he wasn't a detective at the time of the story - he was kicked off the force, because he was framed by his boss. And his boss framed him because he was investigating the killings of local sex offenders, and the chief of police was actually the serial killer wiping them out. And, in the climax of the story, Matt mirrors the chief's rejection of due process by shooting him, execution-style, in lieu of trying to bring him to justice in a corrupted system. And, naturally, this act causes Matt to descend into a supernatural spiral of madness and evil.
It is possible that I have psychological issues about law enforcement.