In Oklahoma and New Mexico, for example, the bar passage rates fell by double digits. Oklahoma’s rate tumbled 11 percent, to 68 percent, and New Mexico’s fell 12 percent, to 72 percent, according to Derek T. Muller, a Pepperdine Law School professor who collects the results and posts them on his blog, Excess of Democracy. Arizona was even lower, with an overall passage rate of 65.7 percent this year.

Law graduates typically can take the test over, and repeaters nudge up the pass rate. But the tumbling outcomes for first-time test takers are spurring debate over whether law schools should be admitting students who score poorly on the entry test. The top scores on the multiple-choice exam are between 156 and 180. Scores below 150 are viewed by many as warnings that test takers lack the skills necessary to practice law.

At least two studies, including one this year that examined admissions exam scores from 2000 to 2011, have concluded that scores on the test, administered by the Law School Admission Council, closely track later bar passage rates.

Mr. McEntee of Law School Transparency, a graduate of Vanderbilt University Law School, said his group’s recent study showed that many schools were admitting students whose lack of legal aptitude made them vulnerable to failing the bar. And, at the same time, they are incurring six-figure student debt that will weigh them down in the future.

The steady erosion in admissions scores between 2010 and 2014, Mr. McEntee, said in his study, is “directly linked to the falling bar exam passage rates in many states.”

One school the study deems as having too many students at high risk is Southern Illinois University School of Law, in Carbondale, Ill. The school, which largely draws its students from Kentucky and Missouri, as well as Illinois, slimmed down its class size to 121 students, from 144 students in 2010. In the last five years, its median law school admissions test score also dropped — to 149 from 153, according to figures it provided to accreditors.

“Our experience has been that someone with a 147 score could pass the bar and someone else with 160 could fail, so we don’t think that there is necessarily a relationship between the test and people’s ability to pass the bar,” said Christopher Behan, the school’s associate dean.