(a) Any offense when he has reasonable cause to believe that such person has committed such offense in his presence; and

(b) A crime when he has reasonable cause to believe that such person has committed such crime, whether in his presence or otherwise. 2. A peace officer acts "pursuant to his special duties" in making an arrest only when the arrest is for:

(a) An offense defined by a statute which such peace officer, by reason of the specialized nature of his particular employment or by express provision of law, is required or authorized to enforce; or

(b) An offense committed or reasonably believed by him to have been committed in such manner or place as to render arrest of the offender by such peace officer under the particular circumstances an integral part of his specialized duties. 3. A peace officer, whether or not he is acting pursuant to his special duties, may arrest a person for an offense committed or believed by him to have been committed within the geographical area of such peace officer's employment, as follows:

(a) He may arrest such person for any offense when such person has in fact committed such offense in his presence; and

(b) He may arrest such person for a felony when he has reasonable cause to believe that such person has committed such felony, whether in his presence or otherwise. 4. A peace officer, when outside the geographical area of his employment, may, anywhere in the state, arrest a person for a felony when he has reasonable cause to believe that such person has there committed such felony in his presence, provided that such arrest is made during or immediately after the allegedly criminal conduct or during the alleged perpetrator's immediate flight therefrom. 5. For the purposes of this section, the "geographical area of employment" of a peace officer is as follows:

(a) The "geographical area of employment" of any peace officer employed as such by any agency of the state consists of the entire state;

(b) The "geographical area of employment" of any peace officer employed as such by an agency of a county, city, town or village consists of (i) such county, city, town or village, as the case may be, and (ii) any other place where he is, at a particular time, acting in the course of his particular duties or employment;

(c) The "geographical area of employment" of any peace officer employed as such by any private organization consists of any place in the state where he is, at a particular time, acting in the course of his particular duties or employment.