sure...well most apartment complexes do not allow you to install such outdoor fixtures, ie screw or attach anything to the outside walls etc.
Some will allow install of a sat dish (by a professional installer only) with prior written permission from landlord/management company and a fee and show proof of Renters Insurance. (for my building the fee is $500 non refundable for sat dish install)
And, well, outdoor roof antenna, yea, they just laugh at you.
They already have each unit wired for cable tv and internet...so...they expect you to use that and you do know that going into the lease.
And how you gonna install a antenna on to the roof if you live say on floor 4 of 10 or something.
If you face the right direction, perhaps you could get away with just setting a small outdoor antenna on your patio/deck, but thats unsightly and not safe or practical.
edit: Says right in that link:
"OTARD rules do not apply to common areas that are owned by a landlord, a community association or jointly by condominium owners. These common areas may include the roof or exterior walls of a multiple dwelling unit. "
I live on 3rd floor of my complex, witch is the top floor, and is flat roof design, so a medium sized latter on my deck and i can get to the roof of the complex....but it still would be a violation for me to install anything up there, or the outside walls, which are stucco. No to mention, drill a hole through the outside walls to run a cable inside...yea...not something I am going to do. not when sticking the large flat antenna i have inside, right over the east facing window in my 2nd bedroom works very well. infact, that position is further in the best direction and angel away from more obstructions than my patio is. And, even if i was allowed to install it out side the window, its a 3rd floor window, with nothing below it. so would need a very tall ladder or special "cheery picker" machine to raise up to that height.
I for sure would not want to live in a complex that allowed tenants to install or do what they want as far antennas go. The risk for severe damage is too high from improper install. Fire risk from lightening strike if not properly grounded, or water damage from screws etc. DIY is not the way to go when you have other dwellings around you to consider. Been plenty of apartment fires and even entire complexes have burned to the ground do to negligent/careless tenants not following the rules. A few happened to buildings in my area many years ago.