Examine the following statements about constructors in Java. Identify the statement that is FALSE based on your understanding of constructor behaviour and syntax.

Let's examine each statement about constructors in Java:

• A. A constructor must have the same name as the class. This is a fundamental rule in Java. Constructors are named identically to their class. This statement is True.
• B. A constructor is automatically called when an object is created. When you use the new keyword to instantiate an object (e.g., MyClass obj = new MyClass();), the constructor is automatically invoked to initialize the object. This statement is True.
• C. A constructor can be overloaded. Just like methods, constructors can be overloaded. This means a class can have multiple constructors with different parameter lists (different signatures). This statement is True.
• D. A constructor must return an object when overloaded. Constructors do not explicitly return any value, not even void. Their purpose is to initialize the state of a newly created object. The new operator is responsible for returning the reference to the newly created object, not the constructor itself. This statement is False.

Therefore, the false statement is D.

The final answer is $\boxed{\text{D}}$.