Matthias Wandel has a pretty extensive history devising ways to trap mice. The winters are long in Canada, and Matthias seems to have no shortage of mice in his shop.
In this episode of Matthias vs. Mice, he sets out to discover how small a hole a mouse can climb through. The answer seems to be somewhere between 16 mm and 17.5 mm, or between 5/8 inch and 11/16 inch in the States.
Turns out, that's about the same limit for a shrew, who invaded the test.
Bottom line: it does not take much of a hole in the siding to open a door to a rodent invasion.
UPDATE:
In a follow-up video, Matthias caught the shrew coming back to try harder—because peanut butter is #worthit.
—You can find Matthias Wandel's videos and articles on woodworking—and more mouse experiments—at his website and on his YouTube channel.