In formal English common law, a person cannot be arrested unless they are in commission of a felony and the person or persons arresting them have observed them committing that felony. In all other cases, by formal law, a warrant of arrest would be needed. Note that there is no need to "arrest" someone to charge and prosecute them for a crime and the expectation under English common law is that a person is only arrested if there is need to do so, such as to identify the person. Otherwise, it is expected that if a person is thought to commit a crime, then what should happen is that they should be indicted, and then summoned to court where they face trial. None of this requires that the person be "arrested", only that it be known who they are, so that they can be summoned.
Obviously, in the modern world the police and the courts ignore this part of common law principles and arrest people on hearsay evidence after the fact, even for misdemeanors. One reason for this is that most states completely immunize police against being sued for false arrest. For example, in New Hampshire there is the following language:
Any claim arising out of an intentional tort, including assault,
battery, false imprisonment, false arrest, intentional mental
distress, malicious prosecution, malicious abuse of process, libel,
slander, misrepresentation, deceit, invasion of privacy, interference
with advantageous relations, or interference with contractual
relations, provided that the employee whose conduct gives rise to the
claim reasonably believes, at the time of the acts or omissions
complained of, that his conduct was lawful, and provided further that
the acts complained of were within the scope of official duties of the
employee for the state.
So, in other words a policeman only has to show that he "reasonably believes" his conduct was lawful to be immune from a lawsuit for false arrest. Furthermore, I believe that New Hampshire's laws against false arrest (that criminalized false arrest) were deleted about 10 years ago.
However, there is a risk for the police in that if they were to engage in false arrest routinely, then there would be a political backlash and the laws against false arrest could be re-instated. For this reason police are cautious about arresting someone unless they have some kind of "reasonable" evidence that the person has committed at least a misdemeanor.
In New Hamsphire, if a person is arrested falsely, the usual course of action is to sue the police for false imprisonment, which is the only law remaining on the books for this kind of action. In some cases, in recent years courts have allowed these civil lawsuits to proceed if the police conduct was particularly egregious. For example, in one case a man was arrested and imprisoned for a long period of time when his drug addict girlfriend trained her 6-year-old daughter to say he raped her. He sued the police for false arrest after his lawyers finally forced the prosecutors to show the girl's record which featured a long list of similar lies against other people. The trial court dismissed the lawsuit, but on appeal the Supreme Court of NH vacated the trial court's ruling and allowed the lawsuit to proceed.