These are the fourteen states (plus the District of Columbia) where over the half the population of that individual state lies within a single metropolitan area (the state-by-state population fractions in largest metropolitan area at the end of the post). And there's not much of a pattern to this. For example, New York, Massachusetts and Rhode Island all grew out of single large population centers that were colonized early on, and this might appear to be a reason for being a city-state. However, Georgia does not have a similar history and is a city-state. On the other hand, Utah was also primarily colonized in a single city, yet is not a city-state.

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