Atwater was stopped for driving without a seatbelt. In Texas (where this took place), this offense carried a possible fine of $25-$50, and no possible jail time. She didn't have her driver's license with her (although her identity was apparently known to the officer who stopped her. Sounds like Lago Vista is a small town). She was arrested for driving without a seatbelt, booked into the jail, and held for an hour before she saw a judge who released her on a $310 bond. She eventually pled guilty to driving without a seatbelt and paid the $50 fine. Then she sued the city.
She sued under §1983 for violation of her 4th Amendment right to be free from unreasonable search and seizure. She argued that her arrest was unreasonable because common law at the time of the framing of the Constitution prohibited warrantless arrests for misdemeanors that were not a breach of the peace, and also because the offense she was charged with was not punishable by imprisonment and there was nothing about the circumstances of her case that made a custodial arrest necessary.
The US Supreme Court makes it clear in their decision that the Justices were convinced this was a contempt of cop arrest. They describe it as a pointless indignity and say that the officer was at best using extremely poor judgment. But they side with the city anyway (just barely, this was a 5-4 decision).
First, the court examines the historical record to try to clarify what the Framers of the Constitution would have meant by "reasonable." It can be really interesting when the court does that, if you've got some extra time on your hands. I'll spare you the long list of examples and tell you that the court decides that 1- the Framers weren't necessarily opposed to warrantless arrests for non-violent misdemeanors, and 2- the historical evolution of law hasn't moved in that direction, either.
Second, the court examines the new rule that Atwater is proposing: that custodial arrests should be made only when an offense is punishable by jail time or when there is some other compelling reason to make a custodial arrest. The court decides that this new rule would be unworkable for a variety of reasons. It's not always readily apparent in the field whether an offense is punishable by jail time or not (such as when the actual weight of drugs seized is close to the line between a minor offense or a more serious one, when the officer doesn't know whether an offense is a first offense or a subsequent offense, or when a sentencing scheme is too complicated to be readily analyzed at the time that an officer is deciding whether or not to make a custodial arrest). Also, turning the exercise of police discretion into a Constitutional question would invite excessive litigation, and would have a chilling effect on enforcement efforts that would outweigh the infrequent benefit of preventing unnecessary (but otherwise lawful) arrests.
Finding Atwater's arguments lacking and her solution unmanageable, the court ruled that "if an officer has probable cause to believe that an individual has committed even a very minor criminal offense in his presence, he may, without violating the Fourth Amendment, arrest the offender." That said, the court noted that the legislature is free to impose statutory restrictions on arrests for minor offenses (by passing a law requiring that a defendant be released on a summons for certain offenses or in certain circumstances).