For example, I live in CA but would like to organize my LLC in MT. Do I need to have my business bank accounts set up and linked to a MT address?
Doesnt matter for Federal Income Taxes, Only State Income Taxes. You will have to report the income in the State where you generate the income and reside. So report the income in California. But, If you do conduct business in Montana then you would have to complete a Non-Resident Tax Return.
Under most circumstances you are allowed to form LLC's in any state you wish, as well as open bank accounts in a different jurisdiction. If you form a state in which you are not a resident, you'll have to appoint a local party to act as registered agent. If you form a Montana LLC, it's not necessary to have an account opened with a Montana branch of a bank. For example, many companies are formed under Delaware law because of the its favorable treatment to businesses, but the company headquarters and operations are generally based in another state. There may, however, be certain rules depending upon what type of business you wish to operate. For example, a law firm may be required to operate a client trust account within the same state, depending upon state & local law.