* Engine: A V6 will have a significantly lower towing capacity than a V8.
* Transmission: Automatic transmissions generally have higher towing capacities than manuals.
* Axle Ratio: Higher numerical axle ratios (e.g., 3.73 vs. 3.08) allow for better towing performance.
* Payload Package: Trucks with a factory-installed towing package will have a higher rated capacity. This often includes a heavier-duty transmission cooler, different rear axle, and other enhancements.
You absolutely MUST check the sticker on the driver's side doorjamb. This sticker will list the GVWR (Gross Vehicle Weight Rating) and the GCWR (Gross Combined Weight Rating). The GCWR is the maximum weight of the truck *plus* the weight of the trailer and its contents. If you exceed this, you risk serious damage to your truck and potentially dangerous driving conditions.
Without knowing the exact specifications of your 1996 Chevy C1500, it's impossible to give a definitive answer. However, expect the towing capacity to likely be in the range of 5,000-8,000 lbs, possibly less if it's a less powerful model. Keep in mind that a car can easily weigh 3,000-4,000 lbs, and adding a trailer adds weight.
In short: It *might* tow a car safely, but you *must* check the sticker and ensure the car and any trailer don't exceed your truck's GCWR. Err on the side of caution – it's better to be safe than sorry.