Yes. By state law, your tax obligation is established on January 1. Even if you move out-of-state the next day, you are still obligated to pay Missouri taxes for the year. State law makes no provision for prorating your tax bill.
A duplicate paid personal property tax receipt may be obtained from the Collector"s office for a fee of $1.00.
The tax responsibility goes to the owner of record on January 1. If property is jointly owned, and the court order dissolving the marriage does not address the tax liability, both parties are jointly responsible for taxes. Neither party can obtain a statement of no taxes due until the tax liability is satisfied.