This is a messy decision but I think its important in that it recognizes the idea that a cellphone can contain a lot of valuable information and allowing the police full access to it incident to arrest has significant privacy implications.

The decision in State v. Smith is here, and the vote was 4–3. The majority’s reasoning is that while you can search a “closed container” found on a person incident to arrest, a cell phone is not a “closed container.”

My cellphone has a large email archive. Allowing the police to go through all of that email in the course of arresting me for, say, DUI, would be a fishing expedition - pure and simple. Its not necessary.

There is an "evidence preservation" argument the state of the cellphone at the moment of arrest might change over time while waiting for a warrant - but this gets you to a "probable cause required but warrant is not required" position, rather than a "search incident to arrest, no standard of suspicion required" position - the police would need to retrospectively establish probable cause to justify a search of the phone.

Incidentally, I think in this case the police possibly had probably cause to look at the call log but I haven't read it carefully.

This result is tangentally relevant to the issue of border searches of laptops in that it acknowledges that the volume of private information held in these devices puts them in a unique category that is different from traditional "containers" that are subject to search in these contexts.

The Volokh Conspiracy - Supreme Court of Ohio Rejects Search of Cell Phone Incident to Arrest