The police know that a crime was committed. They believe that you did it. However, they have no evidence. Can they still arrest you?
Technically, they should not. After all, an arrest requires probable cause. You get probable cause by examining the evidence. The laws are a bit vague — there is no set “amount” of evidence police officers need, for instance, so whether or not they had probable cause can look different from case to case — but the idea is that evidence comes first, establishes probable cause, and then they make the arrest.
That doesn’t mean that the evidence will hold up in court, of course. Maybe an eyewitness made a statement that the police used as evidence. Later, though, it came to light that the eyewitness was intoxicated at the time. Their testimony was unreliable. That evidence could get tossed out of court on those grounds, and, if that’s all they had, you’d be free to go.
All of this deals in technicalities, though. Do arrests happen with no evidence? They do. Officers make mistakes. Some of them abuse their position intentionally. These are illegal arrests, and you can challenge them as such in the legal system, but simply saying that they are illegal does not mean they don’t happen. Illegal activity happens every day, and the police are not immune.
No matter how you get arrested, it’s important to stay calm. Focus on your rights. Talk to your legal team. Don’t say anything that makes the situation worse, and do not resist arrest. Trust that an illegal arrest will get corrected in time and make sure you know exactly what steps you’ll need to take to do it.