Any peace officer of this state in fresh pursuit of a person who is reasonably believed by him to have committed a felony in this state or has committed, or attempted to commit, any criminal offense or traffic infraction in this state in the presence of such officer, or for whom a warrant of arrest is outstanding for a criminal offense, shall have authority to pursue, arrest and hold in custody or cite such person anywhere in this state. All privileges and immunities from liability, exemption from law, ordinances and rules, all pension relief, disability, workmen’s compensation, and other benefits which normally apply to peace officers while they perform their duties in their own jurisdiction shall also apply to them when acting as contemplated above. In addition, this protection shall also be applicable when a peace officer is acting in response to a request for assistance out of his employing jurisdiction. The cost of this protection shall be borne by the individual peace officer’s employing jurisdiction.