946.41 Resisting or obstructing officer.
946.41(1)
(1) Except as provided in subs. (2m) and (2r), whoever knowingly resists or obstructs an officer while such officer is doing any act in an official capacity and with lawful authority is guilty of a Class A misdemeanor.
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946.41(2)(a)
(a) "Obstructs" includes without limitation knowingly giving false information to the officer or knowingly placing physical evidence with intent to mislead the officer in the performance of his or her duty including the service of any summons or civil process.
946.41(2)(b)
(b) "Officer" means a peace officer or other public officer or public employee having the authority by virtue of the officer's or employee's office or employment to take another into custody.
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946.41(2m)(a)
(a) The violator gives false information or places physical evidence with intent to mislead an officer.
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946.41(3)
(3) Whoever by violating this section
hinders, delays or prevents an officer from properly serving or executing any summons or civil process, is civilly liable to the person injured for any actual loss caused thereby and to the officer or the officer's superior for any damages adjudged against either of them by reason thereof.
946.41 - ANNOT.
No law allows officers to arrest for obstruction on a person's refusal to give his or her name. Mere silence is insufficient to constitute obstruction. Henes v. Morrissey, 194 Wis. 2d 339, 533 N.W.2d 802 (1995).
EDIT: One might note that "obstruction" requires one to do something i.e. to give a false name, to hinder, to stop, to delay, to prevent, to place. One must take an action in order to "obstruct".