Can I store items in my apartment?

Solution 1:

Yes you can. I dropped a few things in the apartment the first time I dropped by. A few locations later and a trip back to Detroit and those items are still there.

Be mindful that you don't always have access to the apartment though.

Solution 2:

I'm still in act 1, but I've left a lot of stuff in my apartment. It all seems to be fine, so I may change my answer later.

Personally, I would have loved a storage locker or something. ;)

Update: I'm back in Detroit and all the stuff I left in my apartment is still there. That said though, there have been some interesting resets outside of the place. Broken walls fixed and moveable objects returned to their initial positions.

Solution 3:

Also works with other locations.

I killed the punks behind the gas station gunshop, and dropped my tranq for a shotgun. I got tired of it, sold it, and came back. Tranq was still there.