General Handbook of Instruction No 27 - Book 1A - 2010, pg 142 (pg 145 in .PDF), section 16.2 "Naming and Blessing Children"

The handbook is officially only available to leadership, however a leaked 2010 edition is available here:

http://ge.tt/30Ll6cs1/v/2

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16.2 Naming and Blessing Children

16.2.1 General Guidelines

"Every member of the church of Christ having children is to bring them unto the elders before the church, who are to lay their hands upon them in the name of Jesus Christ, and bless them in his name.” (D&C 20:70). In conformity with this revelation, only Melchizedek Priesthood holders may participate in naming and blessing children. Priesthood leaders should inform members of this instruction before their children are named and blessed. While preserving the sacred nature of the blessing, leaders should make every reasonable effort to avoid embarrassment or offense to individuals or families.

Children are normally named and blessed during fast and testimony meeting in the ward where the parents are members of record.

The following policies apply to blessing babies in special circumstances.

16.2.2 Babies Who Were Born Out of Wedlock

Children who were born out of wedlock may be blessed during fast and testimony meeting. If a family prefers, the bishop may authorize Melchizedek Priesthood holders to bless the child in the home, with a member of the bishopric presiding.

16.2.3 Babies Who Are Critically Ill

If a newborn infant is critically ill, a Melchizedek Priesthood holder or at home without previous authorization from the bishop. A person who does this notifies the bishop promptly so necessary records can be made.

16.2.4 Babies with a Nonmember Parent