[dhosek]

It is a universal practice.

For those baptized in a different church but received into the Catholic church, they will go through a ceremony at the Easter Vigil Mass (where they will typically receive confirmation and first communion) and that church will be their official keeper of records. They will have a copy of whatever proof of baptism the person had. In rare cases where a person was baptized, but there is absolutely no written record (things like an inscription in a family Bible count as written record), they will receive conditional baptism where the person doing the baptism (usually a priest, but not necessarily) will preface the words of the baptism with the phrase, “if you are able to be baptized.” This was the normative practice for those baptized outside the Catholic church before Vatican II. As mentioned in a sibling comment, the baptismal and sacramental records of the church are a key source of genealogical data for many researchers.