if (infowindow.isOpened)
{
   doSomething()
}

if (infowindow.close)
{
   doAnotherthing();
}

function isInfoWindowOpen(infoWindow){
    return (infoWindow.getMap()!=null);
}

if (isInfoWindowOpen(infoWindow)){
    // do something if it is open
} else {
    // do something if it is closed
}

google.maps.InfoWindow.prototype.opened = false;
infoWindow = new google.maps.InfoWindow({content: '<h1> Olá mundo </h1>'});

if(infoWindow.opened){
   // do something
   infoWindow.opened = false;
}
else{
   // do something else
   infoWindow.opened = true;
}