Found it. What a search. You only have to provide ID if you are being detained. The rules for detainment are below and following that is arrest which can occur if you do not provide ID when being detained. Unless they have probable cause to believe you have committed a crime, have a warrant, or actually saw you commit a crime, they cannot detain you and hence, cannot require you to show identification.
Chapter 12.--CITIES AND MUNICIPALITIES
Article 42.--CODE FOR MUNICIPAL COURTS; PROSECUTION AND ARREST
12-4211. Detention; service of complaint and summons. A law enforcement officer may detain a person when:
(a) He or she has a warrant commanding that such person be arrested; or
(b) he or she has reason to believe that a warrant for the person's arrest has been issued by any municipal court; or
(c) he or she has probable cause to believe that the person is committing or has committed a violation of an ordinance, and the law enforcement officer has probable cause to believe that such person will not be apprehended or evidence of the violation of the ordinance will be irretrievably lost unless such person is immediately detained, or such person may cause injury to himself, herself or others or damage to property unless immediately detained; or
(d) any violation of an ordinance has been or is being committed by such person in his or her view.
A law enforcement officer having detained a person pursuant to the preceding paragraph, except subsection (a) or (b) thereof, may release the person or may prepare and serve upon such person a complaint and notice to appear, as provided by K.S.A. 12-4204 or 12-4205 and shall then release such accused person from such detention, except in such instances where the law enforcement officer has power and authority to arrest such accused person as hereinafter set forth.
12-4212. Arrest by law enforcement officer; when authorized. (a) Except as provided in subsection (b), a law enforcement officer may arrest a person under any of the following circumstances:
(1) The officer has a warrant commanding that the person be arrested.
(2) A warrant for the person's arrest has been issued by a municipal court in this state.
(3) The officer has probable cause to believe that the person is committing or has committed a violation of an ordinance and that the person has intentionally inflicted bodily harm to another person.
(4) The law enforcement officer detained the person pursuant to subsection (c) or (d) of K.S.A. 12-4211 and amendments thereto and:
(A) The person refuses to give a written promise to appear in court when served with a notice to appear;
(B) the person is unable to provide identification of self by presenting a valid driver's license or other identification giving equivalent information to the law enforcement officer;
(C) the person is not a resident of the state of Kansas; or
(D) the law enforcement officer has probable cause to believe that the person may cause injury to self or others or may damage property unless immediately arrested.
(b) A law enforcement officer may not arrest a person who is charged only with committing an ordinance traffic infraction or an ordinance cigarette or tobacco infraction unless the person charged has received service of a notice to appear and has failed to appear for the infraction.