Try a web search using the terms
museum board member job descriptions
Here are 3 sample results.
Note - there are generic reference to other non-profit organizations, but also wording specific to museums
http://www.mcn.edu/about/index.asp?subkey=1788
http://www.okmuseums.org/secondary.php?catid=17§ion=9
http://www.ci.irvine.ca.us/pdfs/gpc_board_of_dir_job.pdf
Best wishes, Barbara Hass, retired librarian