Someone’s spitting on my son’s baby carrier in our apartment complex

I live in a old danshi in Japan, and someone's been spitting on my son's baby carrier stored on the ground floor, near the mail boxes.
It's gross and really frustrating.
I want to set up a small camera inside my baby carrier to catch the person, but I'm worried about the legal side of things. Is it okay to do this in a common area?

Any advice or similar experiences? Thanks!