There is no law that would prevent you from recording an interview between you and your client.
However, if you want to use the recording as evidence in a court you can only do so if the client has given consent to the recording. It is therefore a good idea to document that consent.
State based laws will govern the laws relating to recordings, but the general consensus is one of adequate consent being provided. The information may then be used in times of dispute providing that the consent can be satisfactorily demonstrated.
Consideration should also be given to the client’s ability to understand any of the information provided, which cannot be demonstrated in a recording.