Thefts of insured motor vehicles in Mexico rose 3.4 percent last year to 82,510, a new record, an organization representing insurance companies said.

Auto theft has grown 87.5 percent in the country since 2005, AMIS said in a statement.

The group’s director, Recaredo Arias, said May 2011 saw an 18 percent jump in thefts over the same month in 2010, though the annualized increase in December 2011 was only 3.4 percent.

Mexico state, the country’s most-populous jurisdiction, led last year’s figures with 17,672 auto thefts, followed by Nuevo Leon, where thefts soared by 35.2 percent to 13,589.

The Federal District - Mexico City and environs - experienced a 19 percent fall in auto thefts to 11,451.

Authorities recovered 33,604 stolen vehicles in 2011, a gain of 20 percent over the previous year, Arias said. Even so, he added, the proportion of vehicles recovered in 2011, 41 percent, compares unfavorably with the 49 percent rate achieved in 2005.

More than 232,000 of the vehicles stolen since 2005 remain missing, he said.

The proportion of auto thefts involving violence climbed from 47 percent in 2010 to 54 percent last year and in two states, Sinaloa and Zacatecas, violent thefts accounted for 70 percent of the total, according to AMIS statistics.

For the third year running, the Nissan Tsuru was the most-stolen model in 2011, with 14,506 units taken.

Mexico’s insurers paid 9 billion pesos ($681 million) in auto-theft claims last year, AMIS said.