I have my own car I drive to and from work and occasionally on
business. I have two large car magnets that advertise our company's
product that I would like to display on the side of my car, but I am
concerned that this will make my car a "commercial vehicle" and I will
be fined for driving on "parkways" within CT and NY where commercial
vehicles are prohibited. What are the rules and regulations regarding
commercial vehicles on parkways in these two states that would apply
to me?

Many of the signs say "Passenger Cars Only".  I believe the concern is
more about size than use.  Try calling the Westchester County Police
Dept. for clarification.

DMV defines commercial vehicles as follows:
* A single vehicle with a gross vehicle weight rating (GVWR) of 26,001
pounds or more
* A combination of vehicles with a gross combination weight rating
(GCWR) of 26,001 pounds or more if the vehicle(s) being towed has a
GVWR of more than 10,000 pounds
* Vehicles that carry 16 or more passengers, including the driver 
* Any size vehicle that transports hazardous materials
<hazmatreqs.asp> and that requires federal placarding

http://www.dmv.state.va.us/webdoc/citizen/drivers/whatiscdl.asp