Each state has its own laws regarding this topic. In general, if you are selling wholesale to a retailer who will then sell directly to customers then you will not charge sales tax. The retailer will charge the tax. The retailer should have a resale license from their state and be able to provide you with a number you can check online somewhere.
If you are selling to the final customer then you need to follow your states law. In CA I have to collect sales tax for any in state sale. If I am shipping to a customer out of state then I do not charge tax. Now keep in mind there are lots of special circumstances. If you have some type of affiliate in a state that is selling/promoting your product you will be required to collect sales tax for that state if you are shipping to an end customer, not if you are shipping wholesale to a retailer.
Your best course of action is to contact the governing agency in your state and ask them your specific question. They should be able to tell you what your state requires.