If you bought a slave at an auction in the south before the Civil War would you have to pay a tax on that purchase?
Yes, and tax rolls are some of the best sources for doing systematic research into the scale of American slavery.
As Kevin Outterson (then at West Virginia University) wrote in a 2002 paper, "Slave taxes proved to be very valuable: from Colonial times to the Civil War, American governments derived more revenue from slave taxes than from any other source."
(You can find the paper as "Slave Taxes" in Studies in the History of Tax Law, Volume 1.)
Slaves were covered by property taxes, import taxes and occupational taxes. There frequently were taxes for the transfer of slaves and the manumission of slaves. The federal government covered slaves in the Direct Tax of 1798. That act called for property taxes on land, improvements to that land, dwelling-houses, and slaves. The tax per slave was 50 cents.
The direct tax of 1798 was repealed in 1802, but a new direct tax was enacted in 1813, shortly after the United States declared war. Again, slaves were covered under this tax. The tax was increased during and after the war, but after its 1817 repeal, the federal government didn't levy a direct tax again until 1861. Land sales and import duties paid for federal operations between those two years.
Those import duties never included a federal import tax on slaves, even though the provision was written right into the U.S. Constitution: Article I, Section 9, clause 1, states: "The migration or importation of such persons as any of the states now existing shall think proper to admit, shall not be prohibited by the Congress prior to the year 1808, but a tax or duty may be imposed on such importations, not exceeding 10 dollars for each person."
Proposals to begin that tax were brought up in the first Congress, but they were defeated by Southern objections and never were enacted before Congress outlawed the slave trade in 1808.
J. Mills Thornton is one of the better historians to read when it comes to the economics of slavery with regard to taxation. Now retired from the University of Michigan, he's written quite extensively on the issue. You might want to refer to his Archipelagoes of My South: Episodes in the Shaping of a Region, 1830–1965 and Politics and Power in a Slave Society: Alabama, 1800-1860 for further reading.
As Thornton points out in the former book (page 29), "The slave tax constituted some 60 percent of the total receipts in South Carolina and 30 to 40 percent in the others."
At the beginning of the United States, Southern territories and states tended to favor slave taxes that charged a per-person tax. Over time, this shifted to an ad valorum general property tax. By the time of the Civil War, all states but South Carolina had shifted to a general property tax. Archipelagoes of My South covers this in its chapter devoted to fiscal policy.
If you're looking for a short and simple answer to your question, the Montgomery Advertiser wrote a story in February entitled "A permanent wound: How the slave tax warped Alabama finances" that's worth a read.