You may or may not have to pay the tax ON TOP OF THE RENT, some landlords charge it to you and some just take it from the amount you pay - cutting into their profit. You cannot ensure the landlord is paying it (well you could ask them to prove it) and it is not your responsibility to make sure it is paid (an authority will NEVER COME TO YOU LOOKING FOR IT ..). Rental tax (transaction privilege tax) must be paid- REGARDLESS OF HOW LONG THE RENTAL PERIOD IS- by any owner who rents a certain number of properties depending on the city they pay to the city they have the right to collect it form the tenant. If they do not pay they are fined which can be heavy. Property Management companies handle this for their clients (homeowners) and still it only applies to the rules in each particular city where the rental is located. Some smaller cities are regulated by the state.
Feel free to contact me for specifics or further information!