(CNN) -- A new study suggests laws banning the use of hand-held devices while driving have not reduced the rate of accidents in three states and the District of Columbia.

In addition to the nation's capital, the report by the Highway Loss Data Institute reviews insurance claims in New York, Connecticut and California. It also compares the data to other areas that do not have cell phone bans.

"The laws aren't reducing crashes, even though we know that such laws have reduced hand-held phone use, and several studies have established that phoning while driving increases crash risk," said Adrian Lund, president of the Highway Loss Data Institute.

There were no fluctuations in collision rates before and after the laws were put in place, the report said.

"So the new findings don't match what we already know about the risk of phoning and texting while driving," Lund added.

According to the study, the crash rates in the nation's capital were the same as in Virginia and Maryland, which don't have laws limiting the use of cell phones while driving.

Increased rates of crashes when drivers use hand-held cell phones have been well documented, so it's unclear why the four jurisdictions' accident rates did not mirror the trend after their cell phone bans took effect.

Lund said the Highway Loss Data Institute is trying to determine why the ban does not have an impact on the rate of accidents. One of the options is that drivers in jurisdictions that ban cell phones while driving may be resorting to using hands-free devices, whose accident rates are the same as hand-held devices, he said.

"In this case, crashes wouldn't go down because the risk is about the same, regardless of whether the phones are hand-held or hands-free," the study said.

Lund said the new report has left experts puzzled.

"This is surprising, too, given what we know about the growing use of cell phones and the risk of phoning while driving," he said. "We're currently gathering data to figure out this mismatch."

The report comes on the heels of a federal ban on texting for drivers of commercial vehicles such as buses and large trucks. The ban, which was announced Tuesday, is effective immediately.

"This is an important safety step, and we will be taking more to eliminate the threat of distracted driving," said Ray LaHood, the U.S .transportation secretary.

Commercial drivers caught texting while driving face a penalty of up to $2,750.

Last year, the National Safety Council called for a nationwide ban on cell phone use while driving, a prohibition opposed by the industry.

"Studies show that driving while talking on a cell phone is extremely dangerous and puts drivers at a four times greater risk of a crash," said Janet Froetscher, the council's president.

Last year, President Obama also signed an executive order asking federal employees not to text while driving government vehicles. The ban went into effect in December 2009.