Are the apts managed by a company or a single owner? Typically if they are run by a company they will want all your info and run a credit check on you. If on the other hand the apts are run by a single owner then it really depends on the owner/manager if theyll let you leave those sections blank. If it's the latter then your best bet is to know someone who already lives in that complex to put in a good word for you. Show that you won't cause any problems and plan on staying there for a while. Most undocumented families are the best tenants really, they pay cash, always on time, and don't cause any troubles. Most owners know this but their bigotry may prevent them from renting out to individuals in that situation.