In my experience, this is because they conduct yearly x-ray examinations to detect tuberculosis and other lung diseases. Shirts and bras interfere with the image, so they ask students to bring a plain shirt to wear during the examination. However, if there’s no other option, they may ask them to do the examination bare-chested. In my case, there was gender separation (not only in location but also in the time frame), but I can’t say the same for all schools or age groups. Japanese schools are known for having students change into sports clothing in the classroom without gender separation up to 3rd or 4th grade, so I wouldn’t be surprised if there are schools that don’t separate genders for medical examinations.

It’s just the same book divided in two to be more portable.