Good question Jill. Well, we did find information on washing cloth diapers in a laundromat, so we're not sure why you couldn't do the same in your apartment community laundry.
Something to think about is the cost and the effort of washing them if you have to lug them to a basement laundry room in the building. In that case, you may want to look into a diaper service. One thing is for sure - you're going to be doing a lot of laundry.
Readers- please fill us in if you've washed cloth diapers without your own laundry machine and dryer! We're eager to hear your solutions/strategies.
Image via Parents.com.