No, the police do not need a warrant to arrest you. If a crime happens in their presence and they witness it, then they can arrest you. If they show up to a scene and they, based on probable cause, circumstances, and totality of the facts, feel that a crime was committed they can arrest you. In most cases, police make warrantless arrests all the time. For example, if you are driving and a police officer pulls you over and has a suspicion that you are driving under the influence, then they could remove you from the vehicle, ask you to take some tests and if there’s enough evidence to show the police officer that you are indeed intoxicated over the legal limit, he can make an arrest right then and there without a warrant. Another example: if a police officer shows up to your house because there was a call of domestic violence and a witness states that there was domestic violence they don’t need a warrant to arrest you. Those are some examples of warrantless arrests.