I am glad you jumped in here. NY's website does a pretty good job of clearly saying what can and can not be done with a standard DL.
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NYDMV web site isn't always 100% acuate or consistent. This right here is from the New York State CDL training book. Notice the 26001 lbc GCWR with a 10000 lbs trailer. I have found they have a few mistakes.
1.1 - Commercial Motor Vehicles (CMV)
You must have a Commercial Driver License (CDL) to operate any of the following CMVs:
Any single vehicle with a gross vehicle weight rating (GVWR) of 26,001 pounds or more.
A trailer with a GVWR of more than 10,000 pounds if the gross combination weight rating
(GCWR) is 26,001 pounds or more.
A vehicle designed to transport 15 or more passengers (excluding the driver) or a vehicle
defined as a bus under Article 19-A, Section 509-a of the NYS Vehicle and Traffic Law (VTL).
Any size vehicle that is used in the transportation of any material that requires hazardous
materials placards or any quantity of a material listed as a select agent or toxin in 42 CFR 73.
Federal regulations through the Department of Homeland Security require a background check
and fingerprinting for the Hazardous Materials endorsement.
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This is also from the NY web site, again only if combine weight rating is less than 26000 lbs.
桧perator, Class D: Issued to drivers age 18 or over, or to drivers age 17 with Driver Education. Valid for passenger cars and trucks with a gross vehicle weight rating (GVWR) of 26,000 lbs. or less. A Class D driver can drive a vehicle that tows another vehicle (for example a trailer) that has a maximum gross weight of 10,000 lbs. or less. A Class D driver can tow a vehicle with a GVWR of more than 10,000 lbs only if the combined weight rating of the two vehicles is 26,000 lbs. or less. See the important information about changes for Class D drivers that result from a law that eliminates the Non-CDL Class C license.