Funny anecdote: I got a flyer from the University of Phoenix the other day. That's obviously not terribly abnormal...but it was personalized.
To paraphrase, the cover letter said 'hey, we see you've sued someone before! ...wanna be a lawyer? give us money and we'll give you paper.'
I guess they go through court records and send 'targetted advertising' to the addresses they pull (maybe it's just for people who sue someone, or otherwise represent themselves pro se). I dunno, I was tickled by it...UofP, your classiness never disappoints.
Anyhow, I think OP has his answer. You should be able to find any and all state laws through google. There are some good sites that have the code for every state listed for free, but I can't think of the names...google will, though.
This is way too hypothetical, though. A lawyer letter (your C&D) is pretty far from an actual suit being filed. General answer is just that 'yes, you can avoid a summons...for a while.' But you might as well bite the bullet and acknowledge it. If it's a small claims thing, you'd be surprised at how well you can take care of your own ass with a little dedicated research...they aren't sending their super-duper ace crack trial lawyer after you, and small claims/general sessions proceedings are rather informal.
Hiding from their action will only worsen your case. Much better off just talking to their lawyer. I would bet that they could be convinced to leave you alone if they think you have nothing to hide and they have nothing to gain. If they actually sue, you better give your non-compete contract a damn thorough looking over, know what their demands are, and be able to properly evaluate whether you need to seek counsel (depending on the state, they may not be liable for reimbursing your legal expensive whatsoever, even if you win or the case is dismissed).
edit: how are you 'in the clear'? Statues of limitations, AFAIK, are for criminal prosecution. There's probably precedent for civil stuff, but I don't think there are any hard laws in place.
But, for a third or fourth time: laws are based upon the state. There's a reason lawyers generally want nothing to do with advising or pursuing a case outside their own state. I've had actual friends from out of state still pretty much refuse any advice...any question, even in casual discussion, is just met with 'well, I don't know the laws there...'