No. Property tax is separate from income tax. However there may be a similar tax consequence. If you deducted all the property tax, you paid in 2016, on your 2016 federal return and then a got a refund of some of that tax, in 2017, the refund would be taxable income on your 2017 return. The difference is where it gets reported. A taxable refund of local and state income tax is so common, that there is a line for it (line 10*) on form 1040.
Property tax refunds are less common and are reported as "other income" on line 21** of form 1040,
* line 1 of Schedule 1 on 2020 returns
** line 8 of Schedule 1 on 2020 returns
