Attention Sullivan County Property Owners. You Have Until The End Of February To Pay Your 2014 County Property Taxes. Penalties Will Be Charged Beginning March First At A Rate Of 1.5 Percent Per Month. The Trustee’s Office At The Sullivan County Courthouse In Blountville Is Open From 8 A.M. To 5 P.M. Monday Through Friday To Pay Your Taxes. Offices Are Also Located At The Bristol Justice Center And At Kingsport City Hall.