NB: The Catholic Church recognizes all Christian baptisms, whether performed by Protestant, Orthodox, or Evangelical clergy, as long as these are valid in form (trinitarian) and matter (water).
Valid baptisms perfomed by laymen and even non-Christians are also recognized, believe it or not!
I was baptized as an teenager in an Assemblies of God church. When I was reconciled to the Catholic Church, our priest declined to perform another baptism, since my "Evangelical baptism" was done in the name of the Holy Trinity and was thus completely valid. When serious doubt exists as to the validity or correct performance of a previous baptism, a bishop will sometimes authorize a "conditional" Catholic baptism (i.e. "just in case"), but this is rare; the Evangelical church where I was originally baptized didn't even record my baptism, but its validity was accepted by the Church upon my word alone, with the option of obtaining testimony of witnesses (which they did not ask for).