This depends on your buylaws, and charter information. Some assoiciatgion rules apportion the common areas between the home owners, and retain property taxes for only the space occupied by the offices and equipment storage facilities if any.
Others pay common area taxes which become operating expenses.
There is no law in Texas that requires it.
However, if the bilaws and articles of incorporation do not contain any language at all regarding the apportionment of property taxes for the common area, then the assoication would be obligated.
WHy, if there is no law? Because ownership converys the responsibility for taxes. AND, the tenancy relationship between the association and the home owners convey's responsibility for common areas.