Can a state impose an import tax on goods entering from another state?

No, it is forbidden by the US Constitution. But states can impose a "use" tax on its residents, which has the effect of being an import tax.

A "use" tax is a sales tax that the buyer is obligated to pay to the state in which the buyer resides. When a buyer buys goods in another state and has them shipped to the buyer's state, the buyer is supposed to pay his or her state the applicable use tax.

In sales tax, the seller is obligated to collect the tax from the buyer and to pay the collected taxes to the state. In use tax, the buyer is obligated to pay the tax. Recently, California's income tax forms included a line for its residents to report and pay "use" taxes on their out-of-state purchases, and California's use tax rate is currently the same as its sales tax. California recently changed its definition of "retailer" in order to collect unpaid use taxes from on-line retailers who are not collecting use taxes from purchases made by California residents from out-of-state, on-line retailers.

A "use" tax, however, may be unconstitutional if a court finds that it unduly interferes with interstate commerce, as the U. S. Constitution only authorizes Congress to regulate commerce. Since the power to regulate interstate commerce is not expressly granted to the States and only granted to Congress, whether a state tax violates the Constitution's Commerce Clause is dependent on whether a court believes that the state's law, tax, or regulation impedes Congress's ability to regulate interstate commerce. Usually, a state must show a compelling state interest to enact a state law that directly affects and impacts interstate commerce.