I don't remember if it was mentioned in my contract, or if I just looked up state law. I remember when I had a job in Nevada, state law effectively said that work done on my own time, off premises, using my own equipment was mine. I realized that it would be possible to do work on my own time, with their equipment, etc. and I figured if I wanted to avoid a headache it would be my responsibility to make sure I clearly checked all the boxes before I tried to claim ownership.
I can imagine arguments for either side. My point was that you generally want to avoid cases that could go either way. State law said that if I met three criteria, then my employer couldn't claim ownership. I figured that if I only met two criteria, I might or might not end up in a fight with the company. So the solution was to be sure I met all three conditions.
From the company's standpoint, anything I wrote in the scope of my employment, using their equipment, was theirs. And, really, anything I wrote and checked into their source control was obviously something I was saying they had a legal ability to use.
But there is a lot of ground between what is clearly theirs and what is clearly mine, and I believe the best approach is to either avoid that ambiguous ground, or come up with an actual agreement to clarify any vagaries. You want it in writing, but it doesn't have to be an overly-formal contract. It could be a signed letter (from somebody with the authority to give up the company's potential copyright interest; which is probably not your immediate manager).
