SACRAMENTO—The deans of 20 California law schools on Wednesday asked the state Supreme Court to temporarily lower the bar exam’s minimum passing score to let the State Bar study whether the number is unjustifiably high.

The request comes after the pass rate for the summer 2016 test plummeted to 43 percent, the lowest figure for a July sitting in 32 years. First-time test-takers among American Bar Association-accredited schools in California did better—62 percent passed—but still lagged significantly behind their counterparts in other states, including New York, Texas and Ohio.