See, in order to form a partnership there is no need to have written agreement. A partnership can be formed in oral form also.
But it is advisable to have a written agreement where all terms and conditions mutually decided by all partners are categorically written and signed by all partners and registered in the law.
Such written document is called partnership and it is the legal document. If any disputes arises among partners in future. Such disputes are settled on the basis of partnership Deed.
So, partnership deed is not mandatory but advisable to avoid future disputes.