Can self and spouse claim different self occupied properties

I own 2 properties, one jointly with my wife and another with only my name on it. We live in one (owned jointly) and are using the other for storage of unwanted stuff. It has not been rented out. We do not have any loans outstanding on either of the properties.

My question is:

Is it permissible that I claim the unoccupied property as SOP (self occupied property) in my tax return and my wife claims the jointly held property as SOP in her tax return? If this is possible, how do I list the co-owned property in my Schedule HP?

Thanks in advance for your help!!