What you do depends on the type case. Most cases do not require a letter of intent to sue, although that is often sent in hopes that the matter may be settled without the need to file suit.
If a contract requires the notice or if it is a case arising from the violation of a statute, the contract or statute will address whether any notice has to be sent and if so, what time period should elapse before filing suit. (By way of example, generally a landlord must give a Notice to Vacate to a tenant no less than 3 days before filing a complaint for eviction.)
Also, the giving of a required notice is usually complete when deposited in the mail with correct postage and address and actual receipt is not required. (By way of example, although a foreclosure notice is required to be sent to a property owner, the notice is deemed made when the certified mail is deposited in the mailbox.)
You should try to find a lawyer to discuss your matter with you as delay could be putting you in jeopardy of letting a statute of limitation expire.
Note: This response is: a) limited in scope to questions involving Texas law for a Texas resident; b) is intended only as a general information discussion of an issue raised in the question presented; c) does not constitute legal advice as all relevant facts are not known nor analyzed; and d) does not create an attorney-client relationship.
I believe Mr. Wooley's answer is correct.
[In accordance with the Avvo community guidelines, this communication does not constitute "legal advice", nor does it form an attorney-client relationship.]
I respectfully, but thoroughly, disagree with the two lawyers who've left comments here so far.
There's NO general common-law duty to send a "letter of intent" -- which is not a term of art I've seen used in Texas law, "demand letter" is the more typical phrasing -- before you file suit in Texas.
There are, however, certain rights -- typically ones created by statute, and conditioned upon first giving notice and, typically, an opportunity to settle or cure in that notice -- which require it. So whether you need to make a written demand before filing suit depends very much on what kind of claims you intend to bring.
For suits under the Texas Deceptive Trade Practices-Consumer Protection Act, for example (I've linked it below), section 17.505(a) provides:
"As a prerequisite to filing a suit seeking damages under Subdivision (1) of Subsection (b) of Section 17.50 of this subchapter against any person, a consumer shall give written notice to the person at least 60 days before filing the suit advising the person in reasonable detail of the consumer's specific complaint and the amount of economic damages, damages for mental anguish, and expenses, including attorneys' fees, if any, reasonably incurred by the consumer in asserting the claim against the defendant."
It goes on to give the defendant certain inspection and settlement opportunities, with potentially bad consequences if the defendant fails to take advantage.
Similarly, section 38.002 of the Texas Civil Practice & Remedies Code requires as a prerequisite for recovery of attorneys' fees for a contract claim that "payment for the just amount owed must not have been tendered before the expiration of the 30th day after the claim is presented," but you appear to be proceeding without an attorney anyway, and this notice can actually still be given after suit is filed if you ever do get an attorney and seek fees.
Nobody here can tell you whether notice is or isn't required, and if so, how much, without knowing what kind of claim you're making. For many of them, though, no notice is required at all.
Moreover, the question you really meant to ask, I think, is whether you can go ahead and sue while the potential defendant is refusing to pick up his certified mail. Again, to answer that with confidence, we'd need to know more about what kind of claims you propose to file. But in general, it's the SENDING of notice that counts, and if someone buries their head in the sand by refusing to pick it up from the post office, that's their own damn fault and the law isn't going to excuse them.
If notice somehow IS critical: You might want to re-send the same letter NOW by first class mail, since it doesn't have to be signed for. There's a legal presumption, from your testimony that you've sent it, that it was duly received (even if you can't provide first-hand evidence of that, i.e., you didn't see it taken out of the defendant's mailbox and read). The defendant can try to defeat the presumption with his own testimony -- "I never got it" -- but the defendant would have to be able to overcome the legal presumption, and his own lack of credibility may cut against that.