Ninety days is usually how long they'll hold found property before declaring it abandoned, but every police station has their own procedures. You'd have to ask someone who works there. They can also tell you their procedures for disposing of abandoned property. It doesn't sound like you know exactly when they got the safe. It's unlikely police would investigate since it's been a year, but they may allow you to pick it up if you want it. You're free to ask where they got it, but they're probably only going to tell you after you appear to claim it, so consider that if you really think someone may have planted contraband in it.
It would be logical for them to look up the serial number and contact you, but as I said, it's possible that it's just not a priority for them. It's also possible the serial number was damaged, covered up, or filed off. You'd have to ask police why they didn't do that - I'd only be guessing.
To get a warrant, they'd need some reason to think it held something. Like, "This safe was found in a drug house," or the safe smells like marijuana or something like that. Again, it's not likely, and there's no way to really know if that's the case when you have no idea how they received it.
It is possible that you could be charged with a crime based on what was found inside if you claim the safe and show police the contents. I can't think of any reason for you to open the safe in front of the police.