Code:

$ cat Test.java
public class Test  {

    interface Constructor {
        public MyTest execute(int i);
    }

    public class MyTest {
        public MyTest(int i) { System.out.println("Constructor executed " + i); }
    }

    public Constructor getConstructor() {
        return MyTest::new;
    }

    public static void main(String argv[]) {
        new Test().call();
    }

    public void call() {
        MyTest mt = new MyTest(0);

        Constructor c1 = MyTest::new;
        c1.execute(1);

        Constructor c2 = getConstructor();
        c2.execute(2);

        Constructor c3 = new Constructor() {
            public MyTest execute(int i) {
                return new MyTest(3);
            }
        };
        c3.execute(3);

        Constructor c4 = new Constructor() {
            public MyTest execute(int i) {
                Constructor c = MyTest::new;
                return c.execute(i);
            }
        };
        c4.execute(4);
    }
}

It could be compiled sucessfully but then run fails with exception:

$ java Test
Constructor executed 0
Constructor executed 1
Constructor executed 2
Constructor executed 3
Exception in thread "main" java.lang.BootstrapMethodError: call site initialization exception
	at java.lang.invoke.CallSite.makeSite(CallSite.java:328)
	at java.lang.invoke.MethodHandleNatives.linkCallSiteImpl(MethodHandleNatives.java:307)
	at java.lang.invoke.MethodHandleNatives.linkCallSite(MethodHandleNatives.java:297)
	at Test$2.execute(Test.java:38)
	at Test.call(Test.java:42)
	at Test.main(Test.java:17)
Caused by: java.lang.invoke.LambdaConversionException: Type mismatch in captured lambda parameter 0: expecting class Test$2, found class Test
	at java.lang.invoke.AbstractValidatingLambdaMetafactory.validateMetafactoryArgs(AbstractValidatingLambdaMetafactory.java:256)
	at java.lang.invoke.LambdaMetafactory.metafactory(LambdaMetafactory.java:303)
	at java.lang.invoke.CallSite.makeSite(CallSite.java:289)
	... 5 more

That is, java can instantiate object with direct constructor invocation and cannot do this through constructor reference. Should be equivalent access:
JLS 15.13.1. : "treating the method reference expression as if it were a class instance creation expression".
JLS 15.13.3. : "the body of the invocation method has the effect of a class instance creation expression" and "The enclosing instance for the new object, if any, is derived from the site of the method reference expression, as specified in ��15.9.2."
JLS 15.9.2. describes the rules of determining enclosing Instances, and declares compile-time errors in other cases. No run-time errors declared.