Ukuleles, like anything made of wood, are vulnerable to damage through humidity. Experts take the ideal humidity level to be between 45% and 65%. You can gauge the level of humidity where you are using this humidity map.
If you are in the dark blue zone, this means the humidity is too high. This is not such a big problem. Usually, keeping your uke in its case will be enough. If you are concerned about it, silica gel will soak up any excess moisture.
Areas of low humidity, yellow areas on the map, have a larger problem. There is a possibility of cracking particularly if your instrument has come from Hawaii where it is relatively humid. Small instrument humidifiers are quite cheap and are a worthwhile investment.