No. See below:

1) There is no such thing as a "mold-free" certificate.
2) A mold remediation specialist, however, must hold a special license.
3) A homeowner is permitted to perform their own mold remediation work without any license.

***This is confusing because people are saying "you need a mold certificate."***

Homeowners are hearing that to mean that they need a certificate that says their home is free of mold. That DOES NOT EXIST and anyone telling you that you need it is trying to scare and probably scam you. You DO need a "certificate" in the way that certificate is interchangeable with license...because mold remediation specialists must be licensed. But if you are doing the remediation work yourself, as is legally permitted, then there will be no license or certificate and THAT IS OK. It is legal.

The question is simply how confident or comfortable you are in the process. Make sure everything is DRY before you close it back up. The wood moisture should be less than 15% ideally before walls go back up (but absolutely no more than the industry max of 19%). Hire a licensed contractor to perform the rebuilding work. They may make you sign that you personally performed the mold remediation to protect themselves. This is ok too. Document the process you used. Research the industry recommendations (LSU Ag website is a great resource.)

Any document saying that your home is free of mold is only good on the day it was tested. Think about that and you will realize why a "mold-free certificate" makes no sense and is not required to close your walls back up.

Now...when you sell your house down the road? Sure they may require a mold inspection. If the drying process and mold removal products were all correctly used then you should have no problem. You can also talk to your contractor about getting a pest control company in during the rebuild process to treat the walls while they are open. The borate solutions they can apply are also effective at preventing mold growth.