The National Electrical Code requires that all items installed in a building be tested by an NRTL, generally that means UL listed. This does not apply to your personal use items, but does apply to any fixed appliances or electrical equipment that is installed within your home or commercial facility. If your local jurisdiction has adopted the national electrical code then this requirement applies.
Maybe... Assuming this is a mains powered device? There is US Federal law and there are also local laws. If you only sell a few you may get away with not getting a Nationally Recognized Testing Laboratories (NRTL) approval (there are many NRTLs, UL is just the most well known). However, besides pingswept's point, local electrical inspectors may prevent business owners from using your equipment based on local regulations unless they see an NRTL mark (even though the Federal gov may not require it).
Check with the test house that did your CE approval, if they are big enough they may also grant NRTL marks (we use TUV Rheinland). Note that not using UL or CSA may cause problems in some jurisdictions that are old fashioned. We have a $4.5M medical device and the City of Baltimore wanted UL, CSA or MET Labs so we gave MET Labs the TUV test reports and a check for a few thousand dollars and they gave us an approval. UL is a pain to work with, I would go with CSA before UL (even though CSA is Canadian they can grant US NRTL marks in general). Also note that as part of getting an NRTL mark, you will be signing up for periodic (typically four times a year) factory inspections where the NRTL will make sure you are still building your product in the approved way. Of course you pay for that privilege.
http://www.greenexpo365.com/portals/asf0001/resources/intertek/The_Q&A_Guide_for_NA_Product_Certification%28US%29.pdf
I think the bottom line for mains powered equipment is, if you want the US to be a significant market, you want an NRTL approval. While getting the NRTL approval, throw in the Canadian approval, there are only small differences in the requirements and you open up both markets.
Eric
Usually the working voltage between primary and secondary is on the order of a few hundred volts when you're dealing with mains-powered (100-240VAC) equipment. A 500VAC-rated UL recognized cap bridging primary-to-secondary is certainly suitable for this application. 250VAC may be a little on the low side.
Don't expect that just because there's a cap in a reference design publication, the design has ever been evaluated for safety compliance. Quite often, they're not, and the onus is on you to make the design 'safe'.
(Much more common configurations that I've seen are two 250VAC Y-caps in series, or a 250VAC Y-cap in series with a 1kV ceramic.)
UL will care about the part not exceeding its working voltage rating under normal conditions in the application. The dielectric strength test is always much higher than the working voltage rating to account for those 'little things' that can happen in the real world like component failures, lightning strikes, surges, etc. - it doesn't mean that you can and should use a 250VAC cap where the working voltage is 350VAC, for example, even if the part will never fail due to its high dielectric withstand rating.
Best Answer
UL does not approve anything. They publish standards, maintain a list of products that they have tested and/or evaluated to determine that they meet those and other applicable standards, and authorize products that have been listed to be marked with the UL label. In the USA, they are one of several nationally recognized testing laboratories (NRTLs) that provide a similar service. Other NRTLs evaluate products to UL standards, list the products and authorize their own label. In the USA, "approved" means acceptable to the authority having jurisdiction.
There appears to be a standard for information technology equipment (ITE) that allows it to be powered by a listed power supply designed for such equipment without requiring the ITE to be listed.
Golf Carts
In the USA, the standard for golf carts seems to be ANSI Z130.1. There may be NRTLs that will certify conformance with that or manufacturers may assert conformance based on their own evaluation. The standard seems to apply to all aspects of electric motor and engine driven carts.