The more I learn about regulatory compliance, the more I'm convinced that I don't know anything. This is a giant maze of international laws that is difficult to navigate. What I wrote below is just a rough guide, to be taken with a grain of salt. But my last paragraph is very important: You need professional help (not mental help, that I know of anyway).
There are a variety of regulatory standards that you must adhere to. Most of them are going to center around EMI, Electrical Safety, and Materials Safety.
EMI, or Electro-Magnetic-Interference, is concerned with what interference your box is spitting out and receiving either through the air or through the AC power cable. Spitting out would be EMI Emissions, and receiving would be EMI Susceptibility. Emissions is how your box effects other boxes, and susceptibility is more like will your box work when someone is on their cell phone near by. A somewhat related aspect of this is your boxes tolerance to static electricity zaps. In the USA, this falls under the domain of FCC compliance testing. In the EU, it's part of the "CE" approval process.
Electrical Safety is concerned with things like: will your box burst into flames or electrocute the user. In the USA, this is normally certified by an independent lab, like UL or TUV-- I'm not sure about other countries.
Materials Safety is mostly about the use of lead, but does involve a whole list of bad things. In the USA, I'm not even sure there is anyone who cares what's in the device (as long as it isn't medical or food related). In other countries it's referred to as RoHS or other names, but I'm not sure if that falls under "CE approval" or not.
The important thing to know is this: In the practical sense, you cannot self-certify. Doing this compliance testing involves lots of expensive equipment and knowledge and it's simply not practical to do it yourself. Fortunately, there are companies that specialize in this.
Find such a company, and use their expertise to not only perform the tests, but to give you solid information on the whole regulatory compliance testing/reporting process. In many cases these companies will also file all the paperwork with the various government groups, etc. These companies are often well versed in not only your countries regulations, but also international regulations. I'll warn you that this process is not cheap, and not fast. But that's the cost of doing business.
I'm no lawyer, but have been thru the FCC testing process a few times. For a ordinary device that doesn't deliberately transmit (called "unintentional radiator" by the FCC), there is no legal requirement for certifcation. There are legal requirements for what it is allowed to emit, but it up to you how to make sure your device works within the rules.
You can simply sell a unintentionally radiating device without testing. However, if someone files a complaint and the device is found to exceed the legal radiation limits, you're in deep doodoo. If you had the device tested by a accredited test lab and they determined it was within the limits, your legal case will be much better. The FCC still has the right to force you to withdraw the product and even confiscate every unit out there, but if you can show you followed accepted practices of testing then there will be much less of a issue of punative actions.
Intentional radiators are a different story. You do have to have FCC certification to legally sell one in the United States. When the device is certified, you get a certification ID, and that ID generally has to be indicated somewhere on the outside of the device where others can see it.
In the case of a bluetooth module, most likely the module vendor has gotten the certification for the module. If not, I wouldn't go near it. Even if so though, you are still on the hook for the product as a whole. The module will also be certified with some restrictions, like a specific list of antennas that it is certified with. If you attach a different antenna, for example, the module is no longer certified and you're on your own.
If you're trying to sell a intentionally radiating product, you'd better talk to a expert early in the process. You can wing it a bit with unitnentional radiators, but you really don't want to play games with intentional radiators, even if you're using a certified module that does all the intentional radiating.
It might be a good idea to talk to a testing house. They generally will know all the rules. Just keep in mind they sell testing services, and their answers may a bit biased towards you needing a lot of testing.
Best Answer
Due diligence with appropriate certification test reports are necessary for hazardous goods like LiPo packs with all the UN 38.3 test requirements set forth by United Nations.
read http://www.batteryuniversity.com/learn/article/building_a_lithium_ion_pack
Even if shipped by sea, there are risks to damage and supplier packaging test reports must include 1.2m drop tests on all sides and corners. (which may not be enough for some shippers.!)
more details https://www.law.cornell.edu/cfr/text/49/173.185
Also get the UL test report for http://industries.ul.com/consumer-technology/batteries.
I would demand an ongoing Quality reliability verification program with measurable performance and safety parameters and consider large 3rd party liability insurance costs.