Is this person an actual business partner?
Did they and do they bring a valuable asset to the business? They need to provide something you don’t already have. In most cases, this would be: TIME, CAPITAL, EXPERTISE, and EXPERIENCE.
If in fact they are providing one of these and or your business cannot run without them, then you would be wise to formalize it with an agreement.
Also consider: 4 Reasons EVERY Startup Should Consider Partnering