It doesn't in the official oracle JDK source code. Which version are you looking at?
public final class String
implements java.io.Serializable, Comparable<String>, CharSequence
Either way, it wouldn't make a difference whether you wrote extends Object or not in the source code. Beware though, if you had to extend another legitimate class instead of Object, you'll hit a dead end as Java doesn't support multiple inheritence.
Update
The OP is looking at the declaration of String in the API documentation. Every class in Java must and do extend Object. However, it is a different thing whether the source code says extends Object.
The String class doesn't have extends Object in the source code. However, the API declaration always indicates that every class extends Object implicitly.
Have a look at the source code.