If you are leasing a car and you have a co-signer, the account will appear on both your credit report and the co-signer's credit report.
When someone cosigns for an account, they are agreeing to pay the debt if the person they cosign for does not. If you don't make your lease payments, your cosigner has a legal responsibility to make them under the lease contract.
Because your co-signer is equally responsible for the lease, the account and its payment history will appear on both of your credit reports. If you don't pay your car loan as agreed, and the account becomes late, that delinquency will appear on both credit reports and hurt both credit histories.
For that reason, co-signing can be risky, and should be taken very seriously. Whether you are having someone co-sign for you or you are co-signing for someone else, make sure you fully understand the responsibility for all involved. Both parties should understand the impact the debt will have on their credit reports and their credit scores.