To apply for rentista visa do my wife need a birth certificate also ?

You both will need an apostilled BC

Thank you very much for your help. What an apostilled BC ?

First, all your residency (not "visa") application documents must be submitted to Costa Rican Immigration within six months of their issuance, so you both will need new birth certificates and a new marriage certificate. These are typically issued by the Office of Vital Records in the state(s) where they were originally issued (that is, in the states where you were born and married). And they must be "apostilled" by those states.

The apostille process, applied to those newly issued documents, proves that they were legally issued and are valid. The Office of the Great Seal, typically housed in each state's Department of State, usually performs the apostilling process.

These requirements also apply to your financial records that must be included in your residency application and to your criminal background record check.

I should have said above that there are online services which will obtain the necessary documents and have them apostilled for you*. If the website asks, be certain to tell them that you are applying for residency in Costa Rica.

These services act as an intermediary between you and the State that will be issuing your documents and apostilling them. In most states, there is no way to directly address them unless you go to the vital records office in person.

*Nobody said "cheap".