Connecticut filed a lawsuit in August 2005, arguing the government failed to provide adequate funding when it required annual standardized tests for students in grades three through eight. The state wants to test students every other year, in grades four, six and eight.
The high court on Tuesday refused to hear an appeal from Connecticut, which was the first state to challenge the 2002 law.
The NCLB Act bars the federal government from imposing unreimbursed costs on towns and cities.
The case is Connecticut v. Duncan, 10-489.