PROVIDENCE – Just days after Amazon.com did the same, another online retailer has dropped its marketing relationships with Web sites based in Rhode Island in the wake of a sales tax-collection requirement included in the budget signed yesterday by Gov. Donald L. Carcieri.

Overstock.com said it sent notices today to its affiliates in Rhode Island, North Carolina, California and Hawaii informing them that it was ending its affiliate relationships there rather than begin collecting sales tax from customers in the states. The company did not say how many businesses would be affected.

“It’s painful to have to terminate these relationships with affiliates, simply because they live in states where counterproductive (and likely unconstitutional) laws are being passed,” Patrick Byrne, chairman and CEO of Salt Like City-based Overstock (Nasdaq: OSTK), said in a statement.

“However,” he declared, “politicians have to remember that a tax is a price that government charges for a service, and when they raise their prices, we’re going to buy less of their services.”

Rhode Island’s new law requires Overstock, Amazon and other e-retailers to collect taxes on purchases made through the site of a Rhode Island-based author or company. On Monday, Amazon said it was closing the accounts of its affiliates in the state to avoid the mandate.

Overstock previously cut off its affiliates in New York in May 2008 after that state passed a landmark law that would have forced the company to collect sales tax on New York purchases. A lawsuit Overstock filed against the law and another brought by Amazon both are pending.

“When states unwisely and unconstitutionally pass these laws, their local Internet ad business will quickly go dark, and that business will simply migrate to states more friendly to Internet commerce,” said Jonathan Johnson, Overstock’s president. “In the end, the only thing to be accomplished by these laws will be to put more local citizens out of work – exactly the wrong choice in a down economy.”

The dispute stems from a U.S. Supreme Court decision in 1967, reaffirmed in 1992, that said businesses without a physical presence in a state are not required to collect that state’s sales tax. State lawmakers have complained that the precedent is forcing them to forego a growing amount of sales tax revenue that would otherwise be levied on online purchases.

With tax revenue in free fall nationwide, lawmakers in a number of states lately have moved to force online retailers to collect sales tax. They argue that if the retailer has affiliates in a state, it has a physical presence there, and therefore is required to collect sales tax under the Supreme Court precedent. The retailers say that interpretation of the law is faulty.