WASHINGTON — The United States Supreme Court on Monday let stand a ruling from New York’s highest court requiring Internet retailers to collect sales taxes even if they have no physical presence in the state.

As is their custom, the justices gave no reasons for their decision not to hear the case, which involved Amazon.com, the online giant, and a smaller competitor, Overstock.com. The two companies challenged a 2008 state law that required online companies to collect sales taxes on purchases made by New York residents.

Brick-and-mortar companies often complain that they are put at a competitive disadvantage when they are required to collect sales taxes and online companies are not.

In March, the New York Court of Appeals ruled that the companies had a sufficient presence in the state because of affiliated independent sites that linked to the retailers in return for a commission. “The bottom line,” Chief Judge Jonathan Lippman wrote for the majority, “is that if a vendor is paying New York residents to actively solicit business in this state, there is no reason why that vendor should not shoulder the appropriate tax burden.”