Answer:
Like any contractual agreement, it does not HAVE to be in writing, as verbal agreements are technically just as legally binding. However, there is never going to be a situation where not having a written contract is going to be substantially beneficial. Particularly when it comes to running a business with partners, you want to have your contractual relationship solidified, in writing, in the partnership agreement, to avoid disagreement, confusion and possible disputes down the track relating to the terms intially agreed upon.
Especially considering that in a partnership, you are each liable for the debts and actions of the other partners, so you want to be totally clear on your contractual relationship and obligations. A contract lawyer can draft or review a partnership agreement and advise you on your rights as well as in the event of a dispute. It is advisable that each individual partner seek independant legal advice so that fair and equitable terms can be agreed upon.