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Will you have a physical location in each of the three states or just one state? If one state which one? Will you have employees and if so will they work in all three states or just in one state?
I will be working from home which is in Delaware and no employees
You will need a locksmith license from DE and MD to conduct business in those states. You would also register as a business in DE. This can be done online
In MD here is a link that explains what you need to do to get a MD locksmith license. http://locksmithlibrary.com/articles/maryland-locksmith-license-requirements/
You will have to pay sales tax on services you provide in PA but no such tax appears to be payable in MD for your labor. However, if you sell the lock, that will be subject to sales tax so you will need to register for sales tax purposes in MD and PA.
You also may want to incorporate your business so that you insulate your personal assets from the business.
This communication is not intended as legal advice. A local attorney should always be consulted for legal advice. No client/attorney relationship is intended or created by this communication.
PA does not require locksmith to get a license in PA. However you have to be a license locksmith you cannot just be somebody off the street with no training. If you incorporate you would get a federal tax ID number as part of that process. If you operate as a sole proprietor you can use your social security number but I recommend you incorporate as a sub chapter S corp which provides you the protection of limited liability.
You do need to have a license in MD and DE. Those states require licensure under their state license procedures. You do not need a separate license in PA. Your certification is sufficient for PA. I would think that if you are a licensed locksmith in DE it will not be difficult to qualify for a license in MD.