Here are a couple of the codes that I have found concerning burials. From what I have read, you would need to contact the District Atty in the county the babyis buried in and get approval to move the body to SD. I believe you could do this through a funeral home.
I found these at:
http://oklegal.onenet.net/statutes.basic.html
by typing in burial in the search box
§21-1153.
§21-1153.
The last section does not affect the right to carry the dead body of a
human being through this state, or to remove from this state the body
of a person dying within it, for the purpose of burying the same in
another state or territory.
§21-1161.
A. No person shall intentionally remove the dead body of a human being
or any part thereof from the initial site where such dead body is
located for any purpose, unless such removal is authorized by a
district attorney or his authorized representative or medical examiner
or his authorized representative, or is not required to be
investigated pursuant to the provisions of Section 938 of Title 63 of
the Oklahoma Statutes, said authorization by the district attorney or
medical examiner shall not be required prior to the removal of said
body. A district attorney having jurisdiction may refuse to prosecute
a violation of this subsection if the district attorney determines
that circumstances existed which would justify such removal or that
such removal was not an act of malice or wantonness.
B. No person shall remove any part of the dead body of a human being
from any grave or other place where the same has been buried, or from
any place where the same is deposited while awaiting burial, with
intent to sell the same, or to dissect it without authority of law, or
from malice or wantonness.
C. No person shall willfully or with malicious intent violate or cause
damage to the casket or burial vault holding the deceased human
remains.
D. Any person convicted of violating any of the provisions of this
section shall be guilty of a felony and shall be punished by
imprisonment in the State Penitentiary not exceeding five (5) years,
or in the county jail not exceeding one (1) year, or by a fine not
exceeding Five Thousand Dollars ($5,000.00), or by both such fine and
imprisonment.
