You're dealing with Legalese here, and it's a wholly different form of English that is not well understood by the majority of native speakers. A 'deposition' is a spoken statement given by a witness to a crime. An 'affidavit' is the written form of a witness statement. So, it means the officer can take the statements of witnesses, either spoken or written. 'incident to' means in matters related to the officer's job. Whatever those duties are, officers are able to do the listed things, but not in duties that are not associated with their jobs.