A state chartered credit union selling extended warranties must collect sales tax from the customer and remit the sales tax to the Department of Revenue. This is true even though state chartered credit unions are exempt from B&O tax.
However, federally chartered credit unions are not required to collect sales tax or pay B&O tax on sales of extended warranties (or on sales of any other property). However, the purchaser of the extended warranty is subject to use tax on the value of the extended warranty.