The researchers say it does, but that leaves a big mystery. Why have crash rates not zoomed up since cell phones became popular with drivers. Instead the crash/fatality rates have remained much the same over the past 10 years.
Check this article
http://www.drivers.com/article/600/
Also check here
http://www.drivers.com/allarticles/34/

I'm doing a report on whether cell phones should be banned or not while driving. I've found that the U.K. as a country have already put restrictions on the use of cell phones while driving. In the U.S., it varies with the state. Do you think this would have any influence on the crash rate?

As a UK ex-pat living now in USA - and having passed driving tests (first time) in two US States and in the UK... I'd point out that the age for a car driver's permit in the UK is 17 not 18 as reported elsewhere, and that the average mileage traveled by US cars (according to various DOT's and car dealers / Carfax) is between 10 - 12,500 which matches that of the UK. What does not match is the number of accidents and fatalities. In the UK they are near 1/3rd that of the US.. What is interesting is that cars 3+ years old in the UK have stringent tests, of brakes, tires, suspension, mufflers, and all running gear - from wipers to minute cracks in windshields.. whereas as long as your exhaust's clean here you can drive real junkers.. and the steering and braking / handling of many US cars leaves a lot to be desired! I've also met far more drunk drivers here than I did in UK.. where a lost license is exactly that, no 'restricted permits' you have it.. or not! They are also (in UK) much stricter about overtaking on freeways (motorways there) where you only overtake traffic nearer the curb, bot from both sides...

Edgar: The number of fatalities must be compared to the amount of exposure to arrive at a rate that means anything. Accidents per vehicle miles/km (or 100 million for fatalities) traveled is a common measure of accident experience used to objectively rank the safety of a given roadway. Obviously, the authors didn't use this unit frequently used in traffic engineering literature which takes into account that people in certain nations/areas drive more than others. This article is basically meaningless.

Tommy the D: Very few US fatalities involve motorists asleep at the wheel. Also, the facilities with the most fatalities are rural two-lane roadways, while rural four-lane divided interstates normally have the lowest numbers of deaths.

Deaths per 100,000 pop.
USA : 15.8
Canada : 10.3
UK : 6.1
Portugal : 21.1
Japan : 7.9
Germany : 10.7
France : 13.8
Italy : 10.8
Spain : 14.0
Greece : 19.7

In the UK, driver licensing is a strict affair, and expensive, costing thousands of dollars. It isn't taken lightly. And car's brakes and running gear are inspected by law regularly. It is also true that, as one poster said, there are fewer roads such as the US Interstates which can lull a driver to sleep. People just don't take long road trips there, which is where most of the fatalities occur.

What does fatalities per km driven have to do with anything?

What does the square kilometrage have to do with anything? Do you not have numbers on the factor you seem to be attempting to address -- fatalities per km driven?

Do you think that the requirement that the drivers there in Britain have to be 18 years old have anything to do with the crash rate? I think so. And also the public transportation there is wonderful. By the way, I lived there a couple of years and really didn't miss my license because a bus came by within 50 yards of my home every 20 minutes. Young people and the elderly really take advantage of the low price bus fees.

Driving in the UK is fast and roads are crowded, but you've got to pay attention ALL the time. When I drove in Florida a few years ago I found it almost too easy, and hard to concentrate. Almost fell asleep several times!

and...I lot more of them fail to wear seatbelts!