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The city said it rejected the test scores because they were discriminatory, as all but one of the candidates who qualified were white.

Mr. McConnell, Kentucky Republican, said Tuesday that Judge Sotomayor’s ruling in the Ricci case is similar to her work with PRLDEF.

PRLDEF pressed the New York City Police Department to rewrite its civil service exams in the late 1980s, saying the test discriminated against minorities. The NYPD then re-wrote its exam with the help of a PRLDEF-appointed attorney.

It’s unclear where Judge Sotomayor stood on the testing issue and the group’s abortion stance. In other instances her involvment has been more direct, signing onto 1981 PRLDEF letter opposing the death penalty and writing a memo in support of bilingual education.

Group memberships have proved routine fodder for opponents of Supreme Court nominees.

Justice Samuel A. Alito Jr. was hammered on his reported membership in the Concerned Alumni of Princeton, a group that opposed affirmative action policies at the Ivy League school.

Justice Ruth Bader Ginsburg’s work for the ACLU and other women’s rights groups became a point of contention during her 1993 confirmation hearings among senators who questioned her ability to be impartial.

Judge Sotomayor’s confirmation hearing is scheduled to start in the Senate Judiciary Committee on July 13.