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these laws vary from state to state
Also, from county to county. Once again, depending on the state. Some states may have a blanket law that covers all their counties, others do not.
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If he was not the only one living there, the police would need a warrant to search the rest of the house and find anything to "bag" for evidence
Where I live, in Georgia, and in my county, this is kind of how it works. If there is a prospect of a criminal investigation, any evidence uncovered by a search of the home would be thrown out by a court if there was no warrant. Imagine that the cops just waltzed right on in and at some point saw something that indicated that it was a murder. They would play hell getting a warrrant at that time because they had no legal authority to be in the house in the first place. Now, let's say that a judge gives that cop a warrant based on his belief that it was a murder. When it gets to court, a savy lawyer could get the whole case thrown out because the warrant was acquired only after evidence has been found therefore, the warrant was acquired based on evidence gathered without a warrant, hence, none of the evidence is admissable in a court.
O.K., let's say that somebody else lived ther but, was out of country for the week. During the time the cops were in the house they saw a bloody knife in a closet. Without a warrant they can not arrest the other guy when he gets home. They had no search warrant. It makes little sence but, that's law for you. Police cannot get a warrant based on evidence that they should have had a warrant to look for.
Another good one though, not 100% on topic is this, if the cops come to your house with a warrant for someones arrest and find an illegal weapon in your underwear drawer, they cannot charge you with possession of an illegal firearm. They can confiscate it and that's about it. Legally, they had no right to look in your underwear drawer for a person. Now, if during a search through your house for that persons arrest, they happen across that illegal firearm laying in plain site, they can arrest you, confiscate the weapon, and then get a warrant to search for other illegal firearms.
Check with the local laws where you live before you go about playing lawyer in your own defence.