It depends on whether you are creating a corporation or a partnership. The documents you use should be clear on not only what ownership means today, but how ownership changes in the event of something both predictable or unforseen. Consult an attorney as to which documents are appropriate for which corporate structure. Nothing that isn't in writing is "covered." And who is in-charge doesn't have to be the same as who owns a majority.
Very short answer: Of course you need a proper contract. You need to seek legal advise for this from a lawyer.
Depending on what the laws are in your country you might have the following question to answer:
Your co-founder dies unexpectedly (hopefully not), does his/her mother inherit the shares or is his/her 18yo son/daughter sitting with you at the next shareholder meeting? (Who has priority when splitting the now available shares?)
It's an extreme example, but I think it gets the point across.
I wish you best of luck and hope that a lawyer can help you find a good solution, that works for you and your partners.