On September 1st this year we closed on our first rental property. We knew about having to pay of the Real Estate tax at the end of the year, but have yet to get any notice about it. We just checked the status of the bill online and it was supposedly paid off in full today from the previous owner. We assume the previous owner must of had an "auto-pay" set up to pay the bill every year. 

Do we not need to pay the real estate tax until the end of the following year? We have tried calling our county office for the past couple hours, but they are experiencing high call volume and cannot get through to anyone. 

@Alex Helbig

When are county taxes/property taxes due?
Did you check on the closing disclosure, there may have been money held back by the title company to pay for the property taxes.