Picture this: Your Ohio/California/Michigan business provides services to customers nationwide. One day you have an interest from a New York caller. There is email back and force, phone calls, and finally you send your service contract to the New Yorker who signs it and emails it back to you. All the services you provide take place outside of New York. Then the relationship sours and the New Yorker files a lawsuit against you in New York. Can he do that? Can he drag you into a lawsuit far from home, in New York? No, he cannot sue you in New York if the only connection to New York is the fact that he lives in New York and there were emails and phone calls into New York.

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When can a Non-New Yorker be dragged into Court in New York?
You do not have to live in New York in order to be dragged into court in New York. There can be personal jurisdiction over you as a non-New Yorker individual or business if you transact business within New York or supply goods or services in New York. That is what the law says in CPLR 302(a)(1).
A court has said (Fitchburg v Doucet, 9 NY 3d 375, 380):
CPLR 302 (a) (1) jurisdiction is proper even though the defendant never enters New York, so long as the defendant’s activities here were purposeful and there is a substantial relationship between the transaction and the claim asserted. Purposeful activities are those with which a defendant, through volitional acts, “avails itself of the privilege of conducting activities within the forum State, thus invoking the benefits and protections of its laws
Are Emails and Phone Calls enough?
But are emails and phone calls into New York enough? No, telephone calls and written communications, i.e. emails, are generally not enough. Unless they were used on purpose in order to actively participate in business transactions in New York. If all the services you provide are outside of New York and really only the client is from New York, there is no personal jurisdiction in New York.
A court has ruled (Liberatore v Calvino 293 AD2d 217, 220):
Telephone calls and written communications, which generally are held not to provide a sufficient basis for personal jurisdiction under the long-arm statute, must be shown to have been “used by the defendant to actively participate in business transactions in New York”
What should I do if my Customer sues me in New York anyway?
Even though New York courts do not have jurisdiction over you, I would not ignore the lawsuit. The power move is to file a motion to dismiss based on a lack of personal jurisdiction.
See also To Sue or Not to Sue -Evaluating Small Business Litigation