Proposition 47, the 2014 ballot measure that reduced sentences for some theft crimes and drug possession, has not increased the overall crime rate in California as opponents predicted but appears to be linked to a rise in auto break-ins and thefts, a new study says.

Thefts from motor vehicles averaged 16,000 to 17,000 a month statewide before Prop. 47 passed in November 2014 and increased to 19,000 to 20,000 a month in the next two years, the Public Policy Institute of California reported Tuesday, citing state data.

Other types of property crimes, including burglary and shoplifting, increased briefly after the measure passed but then dropped to pre-Prop. 47 levels, the study said. But it said thefts from vehicles did not decline at the same time and were the principal reason for an overall increase in thefts during the two-year period.

“We estimate that Prop. 47 led to a rise in the larceny theft rate of about 135 per 100,000 residents, an increase of close to 9 percent compared to the 2014 rate,” the institute said. It said thefts from motor vehicles accounted for about three-quarters of the increase.

In San Francisco, auto break-ins soared, by 24 percent last year to a total of 31,222, according to police data.

On the other hand, the study also found that Prop. 47 had borne out some of its supporters’ predictions: drops in the prison and jail populations and the costs related to them, and reductions in recidivism, or repeated crimes by people previously convicted of drug and property offenses.

Over the two-year period, the study said, people convicted of those crimes in the past were arrested and convicted less often than similar offenders in earlier years — particularly for crimes covered by Prop. 47, where the decline was more than 10 percent. But the study said some of the difference may have been due to changes in law enforcement practices, as some police departments may have reduced enforcement for crimes such as drug possession.

Prop. 47, whose sponsors included San Francisco District Attorney George Gascón, was approved by nearly 60 percent of the voters. It reduced drug possession to a misdemeanor punishable by no more than a year in jail, ending felony penalties of several years in state prison for some types of drug possession. It also made nonviolent thefts of less than $950 — including shoplifting, check forgery and receiving stolen property — a misdemeanor instead of a felony.

Another study released in March, by researchers at UC Irvine, found that crime in California had increased overall in 2015 but that Prop. 47 was not the cause, because other states with comparable crime rates showed similar rises during that year.

A Los Angeles County prosecutors group, the Association of Deputy District Attorneys, disputed those findings and is backing a proposed November initiative that would repeal parts of Prop. 47. The initiative, which has gathered signatures and is now awaiting approval from state elections officials, would make a third-time theft of $250 or more a felony. It would also allow DNA collection from those convicted of Prop. 47 misdemeanors and would roll back part of Prop. 57, a 2016 ballot measure that made some convicted felons eligible for early parole hearings.

Michele Hanisee, president of the prosecutors’ group, also disputed the conclusion in Tuesday’s report that Prop. 47 had led to lower recidivism rates. She said the reason police were making fewer arrests for crimes such as shoplifting and auto break-ins was that state law prohibits officers from arresting people for misdemeanor crimes that an officer did not personally observe.

“Police can arrest for a felony not in their presence” but not for a theft that is now classified as a misdemeanor, Hanisee said. “For people whose car gets burglarized, the police can do nothing.”

But Gascón’s office noted that, despite the increase in thefts from motor vehicles after Prop. 47, the report found that both property crimes and violent crimes have been declining for several decades in California and remain at their lowest levels since the 1960s.

Bob Egelko is a San Francisco Chronicle staff writer. Email: begelko@sfchronicle.com Twitter: @BobEgelko