Coats should NEVER go under car seat straps!
Sources: Center for Disease Control/Data Statistics, Dept
of Transportation (US), (NHTSA), Traffic Safety Facts
Research Note 2005, Insurance Institute for Highway
Safety, Highway Loss Data Institute
Wearing a coat in the car seat may make the harness too loose to hold your child
in a crash.
 The force of the crash would compress the coat, and your child could
be thrown out of the car seat, and potentially out of the car.

The National Highway Transportation Safety Administration,the Insurance Institute
for Highway Safety, all 50 states and countless child safety organizations warn
parents about the
dangers of bulky coats.

Here are a few of the many warnings on the subject:
More than 1,000 children die year in motor vehicle crashes.  Car seats can save
lives, but
only if they are used correctly.  Just being in the car seat does not
guarantee a child's safety:  in 2005, more than half of the children under 4 years of
age who were killed in car crashes were already in car seats. Almost 80% of car
seats on the roads today have one ore more "fatal misuse errors" which could
increase the risk of injury in a crash (loose installation, loose harnesses, etc.).
The Car Seat Poncho
TM
W e a r    i t    i n    t h e    c a r    s e a t ,    w e a r    i t    o u t    o f    t h e    c a r !
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More warnings about coats in car seats:

CNN, WISC-TV (Madison WI), Safety Mom
Chronicles, Ottawa START, Beacon-Journal
(Akron OH),
Fox News (Cleveland OH),
Cheyenne Regional
Medical Center (WY),
WFAA-TV (Dallas-Ft Worth TX),  CBS News
(Chicago IL),
Babies Online, ABC News
(WHOI-TV, IL),
REMSA (Regional Emergency
Medical Services Authority)