In most cases, condo fees do not include property taxes according to bankrate.com. Fees are paid to the condo board to cover things such as maintenance and the cost of amenities. Owners pay property taxes to local or state agencies as required by tax law.
As with a mortgage on a traditional home, condo mortgages may include prorated tax payments as part of an escrow fund. In such cases, condo owners should not have to make separate payments for property taxes, as those funds would be disbursed from escrow at the appropriate time.
It's important to note the differences between owning a condo and a co-op, because they could impact tax payments. Bankrate.com offers information explaining the differences between owning part of a co-op and owning an actual condo.