If I were to walk into the police station and confess to a crime I did not commit - that wasn't even under investigation - can they arrest or charge me just because I gave a confession?
Neither with or without a warrant, if the confession is all there is. For a felony, the question is whether there is probable cause (4th Amendment). This is true whether the police arrest you, or they get a warrant – the difference being that in the latter case the warrant is issued by a guy with much greater knowledge of what constitutes probable cause. The question then would be whether a confession alone constitutes probable cause. There is a venerable rule, the corpus delecti rule (300+ years old) that requires there to be independent evidence of a crime, the point of this rule being to to prevent mentally ill people from being convicted of a crime that never even happened. Under that rule, a confession alone would not be probable cause (but a confession and a bloody glove could be).
This article reports that at the federal level and in 10 states, there is a lower bar of mere "corroboration" without the need to argue that there was an actual crime. Exemplifying this relaxing of the traditional rule, in Opper v. United States, 348 U.S. 84, the court held that "[a]n accused's extrajudicial admissions of essential facts or elements of the crime, made subsequent to the crime, are of the same character as confessions, and corroboration by independent evidence is required". However, "[t]he corroborative evidence need not be sufficient, independent of the statements, to establish the corpus delicti" and "[i]t is sufficient if the corroboration supports the essential facts admitted sufficiently to justify a jury inference of their truth; but those facts plus the other evidence must be sufficient to find guilt beyond a reasonable doubt". In such jurisdictions, courts take a "totality of circumstances" approach focusing on whether the confession is trustworthy.
I'm sorry, while I'm not a lawyer, I believe Zizouz212 is wrong. -
We know, for a start, that the confession was made to a law enforcement officer and that it was not made under duress.
Thus it can be used to establish probable cause. Further, confessions can be entered for the truth of their contents provided they are used against, rather then for the person making them.
So, yes, a police officer could make an arrest or charge based on the confession - whether they do that on the spot or after further investigation is another issue, and would vary per police department.
Here are some cases/stories which bear this thinking out (granted, they are not in USA) -
They can look into it. Nothing will stop them from that. But to arrest you, they'll need a warrant. To get a warrant, they need to find evidence. Also, the confession you give will never be admissible in a court of law, when the contents of the confession are offered as truth - this is because it wasn't made under oath. However, they can use the confession as a starting point if ever asked why you were being investigated or looked into.
If it was found that you intended to mislead and/or intended to cause problems for the police officers there, or to basically just cause a problem, you may be charged for Obstructing Justice or Public Mischief.