The answer to your question depends on several factors. Form 1099 is actually a family of forms that are used to reports broad categories of income, including interest, dividends, rents, prizes, royalties, and non-employee compensation.
I am going to assume you have a Form 1099-MISC. Whether you have income in another state is going to revolve around the issue of where the income was earned, not where the issuer of the form is located.
For example, if your 1099 is from a publisher, for royalties that you earned by writing a book from your home, you earned that income in your home state. Likewise, if you received non-employee compensation for work that you did online, regardless of where your client is located.
Conversely, if you earned non-employee compensation by crossing the state line to work at your client's facility for several days (or weeks), you earned income in that other state, and will need to file a nonresident income tax return to pay taxes only on what you earned in that state. The same would be true if you earned rents from property located in that state, even if you were never personally present.
