Do both my wife and I have to claim rental income if we both own the house or can just I fill out a T776?

Thank you for your question.

Both of you will need to fill a T776 form.

Each of you need to put your part of income on it and pay tax on this income.

You can read about it at this link:

http://www.cra-arc.gc.ca/tx/bsnss/tpcs/rntl/bt/rprt/menu-eng.html

Have a good day.