The smile on the statue of a Spartan, sometimes assumed to represent Leonidas, is known as the "Archaic smile". It was typical of Greek sculpture in the last century of the Archaic period (c. 600-500 BC).

Inspired by Near Eastern sculpture, introduced to the Greeks through their contacts with Assyrians and Phoenicians in Cyprus, Greek sculptors of the later Archaic peroiod started showing practically all of their human figures with a relaxed, somewhat enigmatic smile on their faces. Here's an example of a male figure from Cyprus; here's a Cypriot lady, now in the National Museum of Antiquities in Leiden, the Netherlands. The style soon spread to mainland Greece; for example, there's the famous statue of the man carrying a sacrificial lamb or the Peplos korê, both from mid-6th century Athens.

That said, the answer to your question is no - there were no other Greek states still making statues in this style at the time the Spartan statue was made. The statue is usually dated to about 450 BC, by which point the Greek world at large had long abandoned the Archaic smile. It is an extremely old-fashioned statue which no Athenian of the time would have been able to sell; in the more fashionable parts of the Greek world, sculpture had transitioned to the so-called "severe style", which generally deployed more natural textures and more movement, but which rarely showed any emotion on the faces of its human figures. Early statues in this style kind of look the same but without the smile, but the development of the "severe style" led within half a century to the production of masterpieces like the discus thrower and the sculptures of the Parthenon frieze.