rental agreement

Not clear.

If you mean "who is responsible for paying bills", it is the person who's name is on the bill.

Do you mean that if you leave a rental apartment, can the landlord then later come after you if it turns out that you have consumed more electricity, water etc than you have paid for (by the monthly provision on top of your rent)? If so, then answer is yes. The landlord has a period of five years to claim any such expenses from you.