The Dubai Municipality will charge you a monthly fee for housing which should be 5 % of your rental agreement. This fee will be added to your DEWA account. If this is not the case you need to go to the Dubai Municipality and fill in a form, with the obvious copies of your rental agreement and passport copies, to make sure they charge you correctly.
If you are the owner of the building you will be charged to going rate for the area which is determined by the "Real Estate Regulatory Authority" (RERA).
For more information on this read this article in the Gulf News