If you are talking about something like a jewelry store robbery, where the police already have an open case, an anonymous tip MIGHT be enough for them to ask a person to voluntarily come in for questioning. It would not be enough, by itself, for them to hold the person or make an arrest. They would have to develop "probable cause" before arresting the person or getting a search warrant, and an anonymous tip is not enough for probable cause; it MUST be corroborated by other evidence. Depending on the answers the person gave during the interrogation/interview, however, probable cause might develop and then they could make an arrest.
If you are talking about a different type of situation, where the anonymous tip is the only report of the crime, it would depend on the circumstances. The information might just go into an "intelligence" file, or if there was a specific reason the police were interested (such as the impact of the crime, or that the alleged criminal is a political figure), they might investigate further, to determine whether there was enough information to open a case. There are also certain "hotline" situations where people can call in anonymously and the police are required to open an initial investigation, but if they question the alleged criminal without any other investigation first, it almost always results in the subject denying the charges and the police closing the case.
Does this answer your question? Although I am not a lawyer, I do have some background in this area.
