According to MO State Statute 137.075 "Persons owning or holding tangible personal property on the 1st day of January shall be liable for taxes." Personal property includes all motor vehicles, motorcycles, recreational vehicles, trailers, boats, motors, mobile homes, aircraft, farm machinery, livestock, and grain.
The Assessor sends out assessment lists January 1 of each year. It is your responsibility to return that list to the Assessor's office by March 1, listing the taxable personal property you own as of January 1 of that year. Under state law, there is no provision for prorating taxes for a partial year, and you will be penalized if the form is not returned to the Assessor's office by March 1.