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.