I have a spray tan machine which I wish to sell in the USA. I have had the machine tested by a CE test house. Do I have to have a UL approval as well?
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.
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.
As far as I know, there is no legislation mandating certification by UL or any other agency, public or private, prior to sale of consumer electrical goods in the US.
The rub comes when one wants to buy product liability insurance and finds that it's unavailable without certification by, say, UL, the reason being that the insurance underwriters are simply unwilling to take the risk of being sued because someone's house burned down because of a rogue widget.
Without some agency like UL and their imprimatur attesting to the safety of the widget, getting goods to market, unless you want to sell them out of the trunk of your car, is going to be difficult, at best.
To add insult to injury, if you manage to get a widget into someone's home and the house burns down, for any reason, the homeowner's lawyers are going to have a field day with you and you're likely to have to spend more time in court than you want to, and even more time on the street, since they'll strip every speck of meat from your bones, just to prove they can.
Insurance companies can not deny coverage based on certification. It's strange as UL or any other certification house will stand by your side if for example a toaster catches fire but you have no recourse against them as they are not liable for the products tested. Hhhhmmmm so why do manufacturers pay for this? And the costs are passed to the consumer. Another way of an private company using scare tactics to make money.