Amazon collects and remits sales tax on behalf of sellers in the following states:

Washington (as of January 2018)

Based on Washington’s Marketplace Facilitator Law, individual sellers are not required to collect and remit sales tax to the state (Amazon will handle that). If you do not have a sales tax permit in the state of Washington and are only selling on a third-party marketplace like Amazon or Etsy, you do not have to collect and remit sales tax on sales that occur on the marketplace. If you have a physical presence in the state and make sales outside of a marketplace, you still need to collect and remit sales tax.

Pennsylvania (as of April 2018)

Based on Pennsylvania’s Marketplace Facilitator Law, individual sellers are not required to collect and remit sales tax  to the state for sales made on an online marketplace. If you do not have a sales tax permit in the state of Pennsylvania and are only selling on Amazon (or Etsy), you do not need a sales tax permit. If you already have a permit, it would be prudential to keep it renewed. For more details, see the interview with Michael Fleming here. If you have a physical presence in the state and make sales outside of a marketplace, you still need to collect and remit sales tax.