How to download the application form to apply for permanent resident in China ?

Do you mean to apply for Permanent Residence Visa（D-type）? if yes, it is issued to a foreign citizen who has been approved by China’s public security authority to reside permanently. That is to say, you need to provide the original of the Confirmation Form of Alien Permanent Residence Status in China for application. Your entrusted relative may apply for the form at the public security organ in the place where you intend to reside.
The application form used for D application is the same as the one for other types, V2011A, which can be found on this site any embassy's website.