So holds New York’s highest court in Tuesday’s Raphael Golb / Dead Sea Scrolls case (though it upheld many of Golb’s other convictions):

Penal Law § 240.30(1)(a) provides that “[a] person is guilty of aggravated harassment in the second degree when, with intent to harass, annoy, threaten or alarm another person, he or she … communicates with a person, anonymously or otherwise, by telephone, by telegraph, or by mail, or by transmitting or delivering any other form of written communication, in a manner likely to cause annoyance or alarm.” We agree with defendant that this statute is unconstitutionally vague and overbroad ….
In People v Dietze (75 NY2d 47 [1989]), this Court struck down a similar harassment statute, former Penal Law § 240.25, which prohibited the use of abusive or obscene language with the intent to harass, annoy or alarm another person. We determined that the statute was unconstitutional under both the State and Federal Constitutions, noting that “any proscription of pure speech must be sharply limited to words which, by their utterance alone, inflict injury or tend naturally to evoke immediate violence.”
The reasoning applied in Dietze applies equally to our analysis of Penal Law § 240.30(1)(a). The statute criminalizes, in broad strokes, any communication that has the intent to annoy. Like the harassment statute at issue in Dietze, “no fair reading” of this statute’s “unqualified terms supports or even suggests the constitutionally necessary limitations on its scope.” See also People v Dupont, 107 AD2d 247, 253 [1st Dept 1985] [observing that the statute’s vagueness is apparent because “[i]t is not clear what is meant by communication ‘in a manner likely to cause annoyance or alarm’ to another person”]). And, as in Dietze, “we decline to incorporate such limitations into the statute by judicial construction” because that would be “tantamount to wholesale revision of the Legislature’s enactment, rather than prudent judicial construction.”
Three federal judges have already found this statute unconstitutional (see Vives v the City of New York, 305 F Supp 2d 289, 299 [SD NY 2003, Scheindlin, J.], revd on other grounds 405 F3d 115 [2d Cir 2004] [“where speech is regulated or proscribed based on its content, the scope of the effected speech must be clearly defined"]; see also Vives 405 F3d 115, 123-124 [2d Cir 2004, Cardamone, J., dissenting in part, concurring in part] [Penal Law § 240.30(1) unconstitutional on its face and as applied]; Schlager v Phillips, 985 F Supp 419, 421 [SD NY 1987, Brieant, J.], revd on other grounds, 166 F3d 439 [2d Cir 1999] [statute is “utterly repugnant to the First Amendment of the United States Constitution and also unconstitutional for vagueness"]).
Accordingly, we conclude that Penal Law § 240.30(1) is unconstitutional under both the State and Federal Constitutions, and we vacate defendants’ convictions on these counts.

Recall that this is the statute that a prosecutor said would be violated even by speech about a person, not just speech to the person:

JUDGE PIGOTT: So if … you get some college kid who write — who e-mails the girlfriend of his roommate saying, you know, he really is a useless person. Is that aggravated harassment with respect to the victim, boyfriend/roommate?
MR. RIVELLESE: Yes, because it’s got —
MR. RIVELLESE: It meets all the elements. It does not require that the person that you send the communication to is the same person that you intend to harass, annoy and alarm. It’s —

For some examples on how such statutes have indeed been read to cover constitutionally protected speech about a person, see this article; the article also talks about how some other criminal harassment statutes have been upheld, if properly worded and if limited to speech to a person (such as harassing telephone calls to the person’s home).