Do I need to file anything with CRA to keep my Roth IRA's tax-free status once I'm a Canadian resident?

Yes. Preserving a Roth IRA's tax-free treatment once you're a Canadian resident isn't automatic, it depends on filing a specific election with CRA, made under the relevant provision of the Canada-US tax treaty, rather than simply assuming Canada will recognize the account's US tax-free status on its own. Without that election, Canada has no built-in reason to treat the account any differently from an ordinary taxable investment account, and its growth or eventual withdrawals could be taxed here.

The election generally needs to be made in connection with your Canadian tax filing for the relevant year, and it's worth doing early rather than after you've already been a resident for some time and potentially missed the appropriate window. Beyond simply filing the election, protecting the ongoing benefit matters too: contributing new money to the Roth IRA after you've become a Canadian resident can undermine the treaty protection for the account going forward, so many advisors recommend treating the account as closed to new contributions once you're a Canadian resident relying on this treatment.

Because getting this wrong can mean losing a genuinely valuable exemption, anyone moving to Canada with an existing Roth IRA should confirm the current election process and timing with an advisor rather than assuming the account looks after itself.