From: The Catechism of the Catholic Church

The Minister of Baptism - Canon Law
Can. 861
#1. The ordinary minister of baptism is a bishop, a presbyter, or a deacon, with out prejudice to the prescript of Can. 530, n.1.

#2. When an ordinary minister is absent or impeded, a catechist or another person designated for this function by the local ordinary, or in a case of necessity any person with the right intention, confers baptism licitly.  Pastor of souls, especially the pastor of a parish, are to be concerned that the Christian faithful are taught the correct way to baptize.

#3. Except in a case of necessity, no one is permitted to confer baptism in the territory of another without the required permission, not even upon his own subjects.

From Catholic Answers:  Why Infant Baptism

Click here for:  Infant Baptism
                      Bautizos de Niños
                      Adult Baptism

Why must I be a registered member of Divine Mercy to have a child baptized here?
Infants are baptized on the faith of their parents.  It is therefore expected that the parents are practicing the catholic faith.  All Catholics living in a particular area are considered to be members of that parish, however, each parish is responsible for insuring that there is an active membership in order to administer the sacraments.  The first question asked when registering a child for Baptism, is are you a member of the parish.  With that we are able to verify active membership and regular participation in the faith.   This is the responsibility given to the church through canon law (canon 868.2). 
The decision to baptize is also a decision by the parents to confirm their active participation and membership in the church.   Registration at a parish indicates a commitment of your family to the parish community.  Active membership is the only way we have of discharging our responsibility in regard to canon 868.2.
 

¿Por qué debo ser miembro registrado de la Divina Misericordia para bautizar a un niño aquí?

Los infantes son bautizados en la fe de sus padres.  Por lo tanto, se espera que los padres estén practicando la fe católica.   Todos los católicos que viven en un área en particular se consideran miembros de esa parroquia, sin embargo, cada parroquia es responsable de asegurar que haya una membresía activa para administrar los sacramentos.  La primera pregunta que se hace cuando se registra a un niño para el bautismo es si usted es miembro de la parroquia.   Con eso podemos verificar la membresía activa y la participación regular en la fe. Esta es la responsabilidad dada a la iglesia a través del derecho canónico (canon 868.2).
 

La decisión de bautizar también es una decisión de los padres para confirmar su participación activa y membresía en la iglesia.  El registro en una parroquia indica el compromiso de su familia con la comunidad parroquial.  La membresía activa es la única forma que tenemos de cumplir con nuestra responsabilidad con respecto al canon 868.2.