You co-signed for your daughter to lease a car What are your responsibilities?

to make sure she pays for it.

More explictly, "co-signing" a loan (of any type) means you are a loan guarrantier - you are equally responsible for the debt that the loan creates. It does NOT mean you have any rights to the item or use of the money that the loan finances; rather, you are legally committing to making sure the loan is repaid, either by yourself or your daughter (in this case).

So, you need to make sure that the loan is paid on time, or it will damage both your daughter's and your credit. If the loan defaults, then the loan originator (creditor) can legally demand payment from both your daughter and you for the outstanding sum of the loan.