Relocating state of Incorporation
Yes, it is possible to redomesticate your Connecticut LLC to Wyoming. The costs vary as there will be a few initial steps required, such as obtaining a certified copy of the Articles of Organization, as well as a Certificate of Good Standing issued less than 30 days prior from Connecticut to be submitted along with the application for Wyoming domestication, where the state also has $100 application fee. You will also need to update the EIN account.
It is not a problem to have an office address in another state. For example, the managing member may move to Washington, and use a home or office address in WA as the business address for the Wyoming entity registration. If you wanted to use a virtual office, you would need to reserve one first, in order to list it on the domestication application. We have a list of providers of this service in our resources section: 'List of providers of U.S. Business Addresses'.
In most states, it is not a problem to establish a business bank account with a bank in a different state than the company domicile. It's always best to check with the banks in the area you plan on conducting your banking in order to find out their exact requirements.