13-2921. Harassment; classification; definition
A. A person commits harassment if, with intent to harass or with knowledge that the person is harassing another person, the person:
1. Anonymously or otherwise communicates or causes a communication with another person by verbal, electronic, mechanical, telegraphic, telephonic or written means in a manner that harasses.
2. Continues to follow another person in or about a public place for no legitimate purpose after being asked to desist.
3. Repeatedly commits an act or acts that harass another person.
4. Surveils or causes another person to surveil a person for no legitimate purpose.
5. On more than one occasion makes a false report to a law enforcement, credit or social service agency.
6. Interferes with the delivery of any public or regulated utility to a person.
B. A person commits harassment against a public officer or employee if the person, with intent to harass, files a nonconsensual lien against any public officer or employee that is not accompanied by an order or a judgment from a court of competent jurisdiction authorizing the filing of the lien or is not issued by a governmental entity or political subdivision or agency pursuant to its statutory authority, a validly licensed utility or water delivery company, a mechanics' lien claimant or an entity created under covenants, conditions, restrictions or declarations affecting real property.
C. Harassment under subsection A is a class 1 misdemeanor. Harassment under subsection B is a class 5 felony.
D. This section does not apply to an otherwise lawful demonstration, assembly or picketing.
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The key here is otherwise lawful. The question would be, since they were intruding in a lawful demonstration, was their demonstration "otherwise lawful?"