AUGUSTA — Crime in Maine increased by 3.6 percent last year, as drug abuse pushed up the incidence of robberies and thefts, the state Department of Public Safety said today. But the statistics also show a decrease in domestic violence for the third consecutive year.

The rates of most crimes, including robbery, burglary, theft, aggravated assault, rape and arson, rose in 2010, Public Safety Commissioner John Morris said. Crimes that saw decreases were domestic violence, auto theft and assault. The number of homicides, 24 homicides in 2010, was two fewer than the 2009 figure.

“Even though Maine continues to be one of the safest states in the country, the increases in robbery, burglary and theft are all a result of drugs,” Morris said.

A recent prescription drug take-back in which 12 tons of prescription drugs were collected by law enforcement across the state points to the level at which people are being prescribed drugs, said Morris. He said the number of drug deaths, most of them due to prescription drugs, exceeds highway deaths in Maine.

“People who are ill with addiction are breaking into homes to get to the medicine cabinet,” said Morris, who wants to convene a working group of doctors, pharmacists, police, educators and treatment professionals to find a solution to the problem.

Rapes and sexual assaults increased in 2010 by 4.3 percent, as the number of reported sexual assault cases rose by 15 to 389.

However, the total number of domestic violence assaults, 5,117 in 2010, represents a 3.3 percent decrease from the previous year, marking the third consecutive year for a decrease in that crime.

“Much progress has been made to reduce violence against women and much of the credit goes to the many support groups available in Maine to help victims,” said Morris.

Overall, Maine remains one of the safest states in the country. Crime figures consistently show Maine to be one of the five safest states in the country, along with New Hampshire and Vermont, said department spokesman Steve McCausland. The violent crime rate in Maine for 2009 was one offense per 1,000 population compared to the national average of 4.3 per 1,000. National figures are typically a year behind state figures.

The Department of Public Safety tabulates the crime numbers based on reported crimes from local, county and state law enforcement agencies. Statewide statistics show that 34,652 crime index offenses reported to police in 2010 compared to 33,411 in 2009, for a total crime rate increase of 3.6 percent.

In rural areas, all crimes showed increases last year except arson and simple assault. Crime in urban areas remained almost the same as the previous year.

The crime rate for violent crime in Maine for 2009 continues to be one offense per 1,000 people compared to the national average of 4.3 per 1,000 for 2009.