The way I read the CPOL Licence
] is that you may use the code, provided you comply with all notices, copyrights, etc., but I see not restriction requiring you to publish the source code to your application because a part of it contains code sourced under the CPOL terms.
However, one clause (5b) states:
"You agree not to advertise or in any way imply that this Work is a product of Your own."
Which to me implies that in order to apply copyright to the application, you would need to clearly state that some parts are subject to copyright by other people, and it would be advisable to list such credits in a easily accessible place, with similar prominence to the copyright notice for the whole work.
You may not at any time claim that the whole work is your own, if you have used and modified code published under the CPOL. However, it may be possible to get permission from the original author to exclude specifics from the "parts of this software are ..." notice.