The correct answer is C. i and iii only.
In order to search a person's home against their will, the police officer would need (i) probable cause, which is the reasonable belief that a crime has been committed or that evidence of a crime can be found in the location to be searched, and (iii) a search warrant, which is a legal document authorized by a judge that permits the police to conduct the search. The signature of the homeowner (ii) is not necessary for a search that is conducted under these conditions.