The Missouri DOR is the agency authorized to assess and collect the monies. Their website states ”You must pay the state sales tax AND any local taxes of the city or county where you live (not where you purchased the vehicle).The state sales tax rate is 4.225 percent and is based on the net purchase price of your vehicle (price after rebates and trade-ins). Use the tax calculator to estimate the amount of tax you will pay when you title and register your new vehicle.
If you bought your vehicle out-of-state and paid taxes on the vehicle to that state, that tax will be credited toward the amount of tax due in Missouri. You must provide proof of the amount of tax you paid in the other state. If the amount of tax paid in the other state is less than the amount owed in Missouri, you will be assessed the difference. If the vehicle was titled in your name in another state for more than 90 days, no Missouri sales tax will be assessed.
Additional information may be found at: http://dor.mo.gov/faq/motorv/general.php#q5