A years-long fight over the release of lawyer admissions data in California could finally be over, after a state court judge ruled Monday that publicizing the information on race and exam scores runs too high a risk of violating privacy rights.

UCLA School of Law Professor Richard H. Sander asked the state bar back in 2006 to disclose the bar exam score, grade point average, LSAT score, race, gender and law school alma mater of everyone who applied for bar admission since 1972. He asked for the data to be given to him without...