Do I need a certificate of coverage to avoid paying both CPP and US Social Security while working remotely?

Yes, a certificate of coverage is generally the mechanism that formally confirms which country's social security system applies to your work, and it's most relevant when a genuinely temporary cross-border work arrangement might otherwise leave it unclear whether CPP or US Social Security should apply. Rather than leaving the question to guesswork or a payroll department's default assumption, the certificate is obtained from the relevant agency in your home country's system and certifies that you remain covered there for the period in question, exempting you from having to also contribute to the other country's system for the same work.

For an ordinary Canadian resident working entirely and permanently from Ontario for a US employer, coverage generally follows where the work is performed, which is more straightforward than a genuinely temporary secondment scenario, but a certificate of coverage can still be useful documentation to have on hand if a US payroll system defaults to withholding Social Security taxes incorrectly, since it provides clear proof of your correct coverage status.

Getting this sorted before contributions start being deducted under the wrong system is considerably easier than trying to unwind incorrect contributions and claim them back after the fact.