There needs to be no investigation, either both his parents are natural born citizens, mean both of they where born on US soil and are US native citizens, not naturalized, then he is eligible, if his parents where not born in the US then he is not eligible to be vice-president, as he would become president if something happened to the sitting president.

It is really an either/or questions. Either they are and he is or they are not and he is not. Really very simple.