Income tax to Canada

Yes, you will continue to pay income tax to the Canadian government.

You really should/need to read the info as a  Non-resident of Canada  especially about the withholding tax.
Also take into consideration, the devalued Canadian Dollar, which means you will lose a lot of your funds ...

Have you previously been to Costa Rica? If not, make sure to visit first a few times, before selling up and making the move. However, it is very different to vacationing here than living here.

Here is the the info for living here legally. It will cost you approx. US$2,500 for the application process for residency and it could take a year or more.

During this time, you will not be covered by the mandatory, socialized medical system

Feel free to contact me via a PM.  We have been here almost 5 years and have some do's and don'ts that I will not make public!
The post above did not answer your question and I will offer the best of a (Canadian non-resident's) ability.
Cheers ....

Please re-read my response to the OP's question regarding paying income  tax on Canadian income, on the first line of my initial post.
I had to reread it myself, to make sure...