A warrantless arrest that begins in a public place is valid:

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A warrantless arrest in a public place is valid if probable cause exists, even if the arrestee retreats to a private place. This is known as the "hot pursuit" doctrine. Good faith and reasonable suspicion may also be factors in the validity of the arrest, but probable cause is the most important factor. Witnessing the flight of the arrestee is not necessary for a valid warrantless arrest.

A Warrantless Arrest That Begins in a Public Place Is