The Legal Services Corporation (LSC) does fund locally-based legal aid services to people in financial need. Although it avoids calling itself a government agency it is funded by the Senate. So for all intents and purposes it is and it does.
Sadly, the Fourth Amendment is not particularly helpful or relevant indetermining when the police can search your car. While it is theoreticallythe starting point of all search/seizure doctrine, the only way to know what the cops can and can't do is to look at the case-law.
I can give you an overview of the Supreme Ct's decisions on carsearches. Note that many state courts have broken with the Supreme Courtin recent years, and may give citizens more protection under the State Constitution than under the Federal. In addition, in each area there are different administrative or other guidelines to control police behavior.
However, in general, I would expect the cops to make full use of the limits of their constitutional powers.
1) Search incident to arrest: _New York v. Belton_ , police have the authority to search the passenger compartment of a car and any containers in it if they are arresting someone recently in that car. _Belton_ said that the police couldn't search the trunk without further justification, but the cops could probably justify a trunk search under a different line of cases.
2) Inventory searches: Anytime the cops tow a car, they can search the car and the contents of any containers inside of it, for inventory purposes. The justification is:
1) to protect the suspect's property,
2) protect the police from claims over lost or stolen property,
3) protect the police from dangerous instrumentalities (bombs in the car, etc.)
The relevant cases are _South Dakota v. Opperman_ and Colorado v. Bertine_. Note that even though this search is supposed to be for inventory purposes, they can use any evidence or contraband they find when they get you in court.
3) Car Searches with probable cause: Under _Chambers v. Maroney_ and U.S. v. Carroll_, the police can search a car whenever they have probable cause. If the cops have probable cause, they can either do the search immediately or tow the car to a police yard, and then do the search. Either
way, no warrant is required. The justification for this is that cars are mobile, and thus the cops can't wait to get a warrant or the car might leave. (I don't like this reasoning either). However, later cases, such as_Texas v. White_ and _California v. Carney_ show that the car doesn't need
to be in motion or stopped on the highway. The Carroll-Chambers rule will apply to any car parked in a public place. There is a limited exception to this for a car parked on a private driveway. Under _Coolidge v. New Hampshire_, the cops would need a warrant if the car is on private property and there is plenty of time to obtain a warrant.
4) Probable cause to search a single container in a car: Under_California v. Acevedo_, the cops can search the entire car (including trunk) whether they have probable cause for the whole car or just for a specific container. As an illustration, if the cop smells marijuana outside your car, s/he has probable cause to believe there is contraband somewhere in
the car. On the other hand, if you walk through the airport and the drug dog sniffs your luggage, and finds contraband, and then you put the luggage in your trunk, the cop only has probable cause to believe there is contraband in your luggage. Under _Acevedo_ this is irrelevant, so the
thinking cop won't arrest you until you get into your car, and they can search both the luggage AND your car.
5) A "frisk" of your car: This is even more vague than the above rules. To make you stop your car, the cops need a "reasonable articulable suspicion" that you are either committing a crime or carrying contraband. Once you
have stopped the cops have per se authority to make you get out of the car (meaning they don't have to justify such a request in any way). Then, the cop can "frisk" your car for weapons, and any containers which might
contain a weapon, if they have "reasonable articulable suspicion" that they might find one. The reasoning is that the cop is in danger, and can search you to protect themselves. A "frisk" of a car is a cursory inspection of locations likely to contain a weapon, analogous to a frisk of a person. The Supreme Court has not defined "weapon" very narrowly, leaving open the possibility that the cops can frisk your car if they see your softball bat on the back seat (This issue has not come up yet). Of course, if the cops happen to find an illegal weapon or contraband, they become endowed with probable cause, and can then go on to perform a full search, or tow your car and search it later.
Generally, I would say that with all of these doctrines allowing
car searches, the police would have to do something blatantly evil before they would be unable to justify searching your car.
Bottom line if they can find probable cause which they determine at the stop then they can search.