The police can, and should, do an inventory sheet, but they are not automatically required to do so by law.  If officers want to claim that they are searching vehicles pursuant to an inventory search, they do need to have a written inventory policy... and most will include a requirement of a written report in the form of an inventory sheet.  An inventory search is an exception to the warrant requirement-- so it's important that officers follow their policies if they do not want the results of the inventory search tossed out during a pre-trial hearing.