first of all, I would say, there is NO static class in java. well, except for static inner class. I thought inner class is definitely not what you meant above there.
You might wanna say, a class that not allowed to be instantiated, with static methods. Like Util classes. i.e. apache common StringUtil...
Static methods in Util classes provide only one implementation. and more important is, it should not know much detailed logic about the passed in Object.
making an example, you have interface:
interface Animal{
int totalLegs(); //here you get the animal object has how many legs
}
then you have Bird, Horse, Warm, Fly classes, implement Animal interface. and they have different impl. of totalLegs. Those implementations are related to detailed logic of the type Animal (Bird, Horse...) so it should go to interface.
And say each Animal has a field Date birthday;
you want to convert the Date to a String with customized pattern. You could create a class, i.e DateUtil and method public static String getDateString(Date d, String pattern){...}
Maybe you could describe a little bit about the interface/impl. in your project. Then we could see if it is better to go to a Util class.