You generally do not need to lead with the referral if recruiting already has it in the system.

If the consultant introduced you directly or gave useful context, it is fine to mention that connection naturally.

Do not overstate the referral as if it should change how the recruiter treats you; the application still needs to stand on its own.

If you are unsure whether the referral attached correctly, that is a separate process question you can ask briefly. For more detail, see the consulting coffee chat guide and the consulting networking guide.

Mine came up naturally when the recruiter asked how I heard about the role.