Multi state S corp filings

The Schedule K-1 is a federal form.  If the state S-Corp return has some sort of its own version, then yes, those will go out to the shareholders as well.

To enter an additional state where your S-Corp earned income, you can follow these steps:

1. Within your tax return, click About Your Business under the Business Info tab
2. Click Edit on the Primarily doing business in: line
3. Click Add Another State
   • If it's not clear in which state you earned more income (roughly 50/50) your business location state is the Primary State

Keep in mind, that not only will you be filing an entity level state return, the shareholder's may also have a filing requirement depending on the respective states income filing threshold.

To avoid nonresidents from having to file a separate individual tax return, many states allow the pass-through entity to file a composite return on behalf of the nonresidents.

Take a look at this for the state(s) you are filing in to see if this is an option.