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Basic Trope: Tension exists between two rival law enforcement agencies over a case or suspect.
Straight: Detectives Alice and Bob of the Tropeville Police Department are prevented from investigating a case by the arrival of Agents Claire and Danny of the FBI, who seize jurisdiction of the case from them. Alice and Bob resent this intrusion.
Exaggerated: The FBI swoops into Tropeville en masse to take over the Tropeville Police Department. The TPD institutes a policy of complete non-cooperation with the FBI.
Downplayed: A traffic cop is about to write a speeding ticket, when a state trooper drives up and takes over.
The case started off as a crime which fell under local jurisdiction, but later discoveries meant that it became a Federal matter. However, the local authorities resent the implication that they need the Federal authorities to 'rescue' them.
Tropeville PD are implicated in the crime itself.
Agents Claire and Danny have a bad attitude when they arrive, acting like they're somehow superior to the 'lowly' detectives and generally acting like a couple of condscending Jerkasses. This behavior naturally makes it more difficult to work with them.
The Tropeville Police Department seize jurisdiction of the case from the FBI.
Variant: Neither police department wants the case, and tries to find justifications why the other department should take care of it.
As the case progresses, the FBI take an interest in the case, but decide not to take jurisdiction and leave it up to the Tropeville Police Department.
The Tropeville Police Department welcomes the FBI taking jurisdiction with open arms.
The FBI change their mind when the Tropeville Police Department fail to make progress.
Tension gradually builds up, however, and soon the rival investigators are at each other's throats.
The arrival of Agents Claire and Danny, along with the rest of the FBI, provokes an actual fistfight between the FBI and the Tropeville Police Department. At the crime scene.
Dozens of organizations ranging from the local police to the school board fight each other over who has jurisdiction in the case.
Tropeville Police Department get along horribly with the state cops but get along fine with the FBI. They really love the Department of Alcohol, Tobacco and Firearms.
Alice contacted the FBI in the first place and wants to cooperate with them so that the case will be solved faster. Bob, however, is not happy about it, especially since Claire acts like she's superior to everyone. Her partner Danny, however, proves more reasonable and helpful, and they develop a better understanding and respect for each other while working the case. On the other hand, Claire's snippy behavior makes Alice reluctant to call the FBI for help in the future, as she doesn't look forward to the prospect of potentially having to work with her again...
Averted: There is no jurisdiction tension in the case at hand. Bob might even state that they're glad the FBI is here.
Enforced: The writers are interested in the conflict that exists between different law enforcement departments.
Lampshaded: "Agent Bradley, FBI. We're taking over this case; should we start bickering now, Detective, or would you rather catch the bad guy first?"
Invoked: Alice and Bob suspect that corruption within the department could be involved in their current case, and so contact the FBI in order to ensure that the bad guys are caught without interference from corrupt locals.
Defied: Alice and Bob conspire to ensure that the FBI never find out about the case, fearing they'd seize jurisdiction.
Discussed: "I hope you didn't hit any mailboxes during that car chase Detective, otherwise the Feds will be all over us."
Conversed: "Ever notice how on Police Procedurals, the cops and the feds always hate each other's guts?"
Deconstructed: The infighting between the FBI and the local police only serves to stall the investigation and give the killer the chance to cover their tracks and avoid punishment.
Reconstructed: The police accept that the FBI have jurisdiction and in the interests of justice cooperate, but this doesn't stop them from making snarky comments at their rivals.
Played for Laughs: The rivalry between the FBI and the local police takes on petty, childish tones.
Played for Drama:
The killer works to play the FBI and the local police off each other in order to keep acting with impunity.
Following the "Defied" example, the FBI learns about the case anyway. Because Alice and Bob were trying to hide information from them, they immediately assume the worst: that they're somehow involved in the original crime and were trying to cover up their own corruption. Now the two detectives have to deal with hostile and suspicious agents picking apart their every move, trying to find any flaws and failings they can use to get the pair fired...
Police Officer: Go back to Jurisdiction Friction, before those FBI numbnuts start flashing badges everywhere. FBI Agent: Oh, go back to your tractor, ya hick. If you cops could handle a trope page, we wouldn't need to be here.