I'm using Piwik for my multiple websites. Installed it on shared server.
I wonder, is there any possibility that this tool transfers my websites' statistics to third party servers such as application owner's servers? How can I check this tool for this reason?
Your data is never shared with anyone. Here is the explanation from Piwik's privacy page
Piwik ensures the Privacy of your Users and Analytics data. When using Piwik, YOU keep control of your data, nobody else does. Your data is stored in your own Mysql Database, and logs or reports data will never be sent to other servers by Piwik.