It's safe to assume Powell hears at least part of what Egon and crew are explaining to each other and the assorted men in lock-up about what's happening, and that includes a Sumerian god showing up to destroy humankind. That's a hell of a lot of crap to take at work. And of course you'd never believe it, unless you were in New York at the time, where walls are bleeding and the dead are routinely covering people in ghost snot. Al Powell would have no reason not to believe what these four men, summoned by the mayor himself, are saying.
If we know nothing else about Powell, we know he's a talkative man -- it's a key aspect of his character in Die Hard (we'll get to that shortly). So he probably would have chatted with the Ghostbusters and got their side of what was happening, including the layman's explanation Egon already offered earlier in the film, aka the Twinkie.
Thus begins Powell's long and deranged obsession with the Twinkie. The Twinkie that, over time, comes to represent evil and badness in his mind. The Twinkie is where horror comes from. The Twinkie must be contained.
Since Al Powell is already at the mayor's office when the Ghostbusters say they need an escort to Central Park West, he would also be at the scene when Gozer comes back in the form of a 100-foot-tall Marshmallow man. In the span of a day Powell has come to learn definitively that there is an afterlife and it's not necessarily a pleasant one, and also that demonic, trans-dimensional gymnasts could, at any moment, cross into our reality and kill us all in the most comical way Dan Aykroyd can think of. This is more than a simple beat officer is meant to be able to deal with.