If you invoked the fifth, you'd be made fun of, since that's a US thing.
But section 7 of the Charter of Rights and Freedoms:
> Everyone has the right to life, liberty and security of the person and the right not to be deprived thereof except in accordance with the principles of fundamental justice.
has been found to provide similar protections. You can be required to identify yourself, and, in drunk driving cases, you can be required to do roadside sobriety tests, but in general, you aren't obliged to answer questions from the police.