I don't know where I can find a rigorous statistics course or textbook. The closest thing I can think of is measure-theoretic probability theory, but I wouldn't really call that "statistics". By 'close to statistics', I mean something that, although as mathematically rigorous as probability theory, can be reasonably substituted for a statistics course with minimal study.
Does such a thing exist? Perhaps not, as the point of many statistics courses is in their applications.