java.io.DataInput.readUTF() and java.io.DataOutput.writeUTF(String) say that a String object is represented by two bytes of length information and the modified UTF-8 representation of every character in the string. This concludes that the length of String is limited by the number of bytes of the modified UTF-8 representation of the string when used with DataInput and DataOutput.
In addition, The specification of CONSTANT_Utf8_info found in the Java virtual machine specification defines the structure as follows.
You can find that the size of 'length' is two bytes.
That the return type of a certain method (e.g. String.length()) is int does not always mean that its allowed maximum value is Integer.MAX_VALUE. Instead, in most cases, int is chosen just for performance reasons. The Java language specification says that integers whose size is smaller than that of int are converted to int before calculation (if my memory serves me correctly) and it is one reason to choose int when there is no special reason.
The maximum length at compilation time is at most 65536. Note again that the length is the number of bytes of the modified UTF-8 representation, not the number of characters in a String object.
String objects may be able to have much more characters at runtime. However, if you want to use String objects with DataInput and DataOutput interfaces, it is better to avoid using too long String objects. I found this limitation when I implemented Objective-C equivalents of DataInput.readUTF() and DataOutput.writeUTF(String).