This is by Anton Strout.
The word that kept popping into my head while I read this was "silly". I have no idea if that was intended or not!
The main character has the ability to touch an object and see what's happened around it in the past, which makes normal relationships difficult 'cuz he keeps ending up knowing more than he ought. He works for a secret government group that takes care of the paranormal goings on in NYC. The department names are all ridiculous, there's the "Things that go bump in the night division", the "fraternal order of goodness"... they're all just kinda goofy. It's this weird combination of government bureaucracy and psychics and ghosts.
Plot-wise... a ghost shows up and needs help but doesn't remember anything about who she is. So our hero has to figure out how to help her and finds an evil organization along the way. And it's just as weird as the one he works for, all office workers and red tape and clipboards. It's silly!