The SCOTUS has ruled on this and such a statute would be unconstitutional
http://caselaw.lp.findlaw.com/scripts/getcase.pl?court=US&vol=482&invol=451 Second, contrary to the city's contention, the First Amendment protects a significant amount of verbal criticism and challenge directed at police officers. "Speech is often provocative and challenging. . . . is nevertheless protected against censorship or punishment, unless shown likely to produce a clear and present danger of a serious substantive evil that rises far above public inconvenience, annoyance, or unrest." Terminiello v. Chicago, 337 U.S. 1, 4 (1949). In Lewis v. City of New Orleans, 415 U.S. 130 (1974), for example, the appellant was found to have yelled obscenities and threats at an officer who had asked appellant's husband to produce his driver's license. Appellant was convicted under a municipal ordinance that made it a crime "`for any person wantonly to curse or revile or to use obscene or opprobrious language toward or with reference to any member of the city police while in the actual performance of his duty.'" Id., at 132 (citation omitted). We vacated the conviction and invalidated the ordinance as facially overbroad. Critical to our decision was the fact that the ordinance "punishe only spoken words" and was not limited in scope to fighting words that "`by their very utterance <482 U.S. 451, 462> inflict injury or tend to incite an immediate breach of the peace.'" Id., at 133, quoting Gooding v. Wilson, 405 U.S. 518, 525 (1972); see also ibid. (Georgia breach-of-peace statute not limited to fighting words held facially invalid). Moreover, in a concurring opinion in Lewis, JUSTICE POWELL suggested that even the "fighting words" exception recognized in Chaplinsky v. New Hampshire, 315 U.S. 568 (1942), might require a narrower application in cases involving words addressed to a police officer, because "a properly trained officer may reasonably be expected to `exercise a higher degree of restraint' than the average citizen, and thus be less likely to respond belligerently to `fighting words.'" 415 U.S., at 135 (citation omitted).
The Houston ordinance is much more sweeping than the municipal ordinance struck down in Lewis. It is not limited to fighting words nor even to obscene or opprobrious language, but prohibits speech that "in any manner . . . interrupts" an officer. 10 The Constitution does not allow such speech to be made a crime. 11 The freedom of individuals verbally <482 U.S. 451, 463> to oppose or challenge police action without thereby risking arrest is one of the principal characteristics by which we distinguish a free nation from a police state. 12 <482 U.S. 451, 464>