If your partnership is going out of business, you want to formally dissolve the partnership to make sure that your liability for partnership debts ends and that one of your partners can no longer bind you to a business deal (making you personally liable for it) without your knowledge or agreement.
First, you and your business partners need to vote to dissolve the partnership. Record the decision in writing.
You'll want to discuss the responsibilities of each partner regarding the debts and any future liabilities of the partnership. For instance, if Partner #1 pays off his half of the partnership's debt but Partner #2 fails to pay off his half (or files for bankruptcy), creditors can still come after Partner #1 for the rest of the partnership's debts.
If your partnership is insolvent, consult a lawyer. If there aren't enough business funds to pay partnership debts and liabilities, the partners should seek the advice of a business lawyer to protect their interests. Connect with a local business lawyer.
Be sure to record your agreements regarding how you'll handle present and future liabilities in writing. Without a written agreement that one partner was to pay a certain portion of the debt, or to pay a certain debt, the other partners are still liable for that partners debt and can be sued for the full amount. Even with a written agreement, in the above example, if Partner #2 fails to pay his share of the debt, and he has no assets or files for bankruptcy, Partner #1 might not be able to collect any money from him. That's why it makes sense to hire a lawyer if the partnership itself can't pay all of its debts before folding.
It's a good idea to file your state's dissolution of partnership form (available from your state's secretary of state or corporations division website) as additional proof that the partnership has been terminated. Typically, filing a partnership dissolution form with the state isn't legally required unless you filed paperwork with the state when you formed your partnership. (For instance, in California, a partnership needs to file a certificate of dissolution form only if it filed a statement of authority with the secretary of state when the partners formed the partnership.) But, to make it clear that you are no longer in a partnership or liable for its debts, it makes sense to file the partnership dissolution form anyway.
It also makes sense to publish a notice in the local newspaper that your partnership is no longer in business. This puts creditors on notice that the partnership, as well as any of the partners, can no longer incur debts. This is especially important for partnerships, because any partner can bind the partnership to a deal without letting the other partners know. You could be on the hook for debts you don't know about.
These are only the technical steps of winding down your partnership. There are many other practical steps to closing your business that can affect your future liability: notifying your creditors, liquidating and distributing the business's assets, and negotiating the settlement of partnership debts with creditors. For more information, see our section on Going Out of Business.