If the city resides within the same county, a couple of things can happen here. 1. The city can have an MOA (Memorandum Of Agreement) with the county agency. This basically says that the county agency gives permission for the city agency to conduct its law enforcement business (xxx) amount of miles or feet from the city line. This effectively extends the jurisdictional boundaries of the city agency. You see this alot with city agencies who may be very small as far as crime and incidents compared to the county from which they reside in. An example is a city cruiser that is sitting on the side of the road, operating radar a mile from the city limit. 2. The city officer can be a member or part of a Warrant/Fugitive Task Force. These units in general gather officers/deputies from several municipal and county agencies to form one unit that can go anywhere in that county (sometimes the state if a state trooper is involved) to arrest, search and seize subjects, property, execute search warrants and recover contraband. 3. The officer could be "deputized" by the local sheriff to conduct his/her law enforcement duties. Basically the city officer gets a temporary rank of "deputy", to conduct his/her law enforcement duties outside the city limits but within the county. Once completed, the "deputized" title is removed. So to answer your question. Yes, more than likely that city officer can apply for a search warrant in the county but outside the city and execute it.