Well, generally speaking, you can wear contact lenses and reading glasses at the same time. As we know that contact lenses is make of special materials, such as some plastics. And contact lenses are applied directly in your eyes, and they can touch your eye ball directly. On the other hand, reading glasses can heavier than contacts. But it does not matter, whether you wear both of them or not. But you should know that by wearing both of them, it will increase the risk of getting the eye strain. And some people even can not be accustomed to the high eye pressure. So you should ask some advices from doctor.
In my own opinion, you'd better not do this at the same time by wearing the contact lenses and the reading glasses which will be bad for your eyes. If you don't use the contact lenses as the vision help, you'd better not wear it because it may make your eyes become dry. And your eyes may get high possibility of infection.