By law they can randomly show up to your apartment unannounced. But its illegal for them to walk right into your apartment without your permission. If Police need a warrant , they will need one as well.

My friend gets monthly inspections as well, the managers walk around knocking on doors, if no answer they move on. If after 2 attempts of knocking they send out a letter and tape it to the door stating you must be here on this day or eviction is put in place.