The best answer is: no ... maybe ... yes ... it depends.
'no' - I did not find a requirement for a sink in each exam room in the "building codes"; however; the "building codes" are not the only governing requirements, and some of those other requirements indicate the 'yes'/'maybe'/'it depends' answers.
Here are some links which may guide you to your final answer, but my take is: yes, put a hand washing sink in each exam room during construction or renovation, rather than have to do it later at greater expense:
(place cursor/mouse over link, right click, select 'Open in new tab')
'yes' -
http://www.ahcaseminar.com/Speaker%20pd ... pitals.pdf 'yes' -
https://www.jointcommission.org/standar ... d=&print=y 'maybe'/'it dpends' -
http://blogs.hcpro.com/osha/2009/04/ask ... xam-rooms/ Hopefully, the above will help guide you in the right direction toward the your answer.