According to Taiwan law, every foreigner and his/her dependant family members over the age of 6 must applying for an Alien Residence Certificate (ARC) must undergo a medical check-up as part of the application process.  This examination will include: chest x-ray and checks/tests for blood pressure, body height and weight, urine and stool samples, and a HIV blood test.  When registering for an ARC check-up, applicants should be sure to specify to this to the hospital, to differentiate between a normal medical check-up. 

A number of Taichung hospitals are government authorized to provide these ARC check-ups, including: China Medical College Hospital, Taichung Hospital, and Taichung Veterans Hospital (see following list).  The cost for a check-up is around NT$1,800 and each person needs to bring their passport and about three passport-size photographs.  Usually, a hospital will issue an official ARC medical check-up report (which needs to be picked up) within a week after the check-up is conducted, so ARC applicants should plan accordingly.

More information about ARC check-ups is available at: http://www.boca.gov.tw

Links: List of Local Hospitals