Lender policies on the source of funds for your down payment can vary but if you are a joint holder on the account being used for your down payment then you should not need a gift letter. Please note that there are two types of joint accounts -- "and" joint accounts and "or" joint accounts. With an "and" joint account the account holders are listed as "Account Holder 1" and "Account Holder 2" on the account documentation. With an "or" joint account the account holders are listed as "Account Holder 1" or "Account Holder 2". With an "and" joint account, both account holders are required to sign checks or approve wire transfers from the account. With an "or" joint account, only one account holder is required to sign checks or approve wire transfers. You should understand what type of joint account you have because your relative may be required to sign the check or approve the wire transfer for your down payment.
Another point that you should be aware of is that it is helpful if the funds in the account that are being used for the down payment are "seasoned" which means the money has been in the account for at least two months. Most lenders require that you provide two months of bank statements when you apply for a mortgage. If the money you are using for a down payment has been in the bank account for more than two months (so the funds appear on both monthly bank statements) you should be good to move forward. If the down payment funds have been in the account for less then two months and a large deposit appears on one of the monthly account statements then most lenders require a letter explaining the source of the funds as lenders usually have policies in place to verify that the funds come from a legitimate and legal source.
Providing an explanation of the source of funds, or even a down payment gift letter, are manageable requirements when you apply for a mortgage but the process goes more smoothly if you can avoid that additional documentation. We provide a thorough overview of the Down Payment Required for Mortgage on FREEandCLEAR that may be helpful for you to review.