California Code of Civil Procedure Section 2036

2036.  (a) If an appeal has been taken from a judgment entered by
any court of the State of California, or if the time for taking an
appeal has not expired, a party may obtain discovery within the scope
delimited by Section 2017, and subject  to the restrictions set
forth in Section 2019, for the purpose of perpetuating testimony or
preserving information for use in the event of further proceedings in
that court.
   (b) The methods available for discovery for the purpose set forth
in subdivision (a) are (1) oral and written depositions, (2)
inspections of documents, things, and places, and (3) physical and
mental examinations.
   (c) A party who desires to obtain discovery pending appeal shall
obtain leave of the court that entered the judgment.  This motion
shall be made on the same notice to and service of parties as is
required for discovery sought in an action pending in that court.
   (d) The motion for leave to conduct discovery pending appeal shall
set forth (1) the names and addresses of the natural persons or
organizations from whom the discovery is being sought, (2) the
particular discovery methods described in subdivision (b) for which
authorization is being sought, and (3) the reasons for perpetuating
testimony or preserving evidence.
   (e) If the court determines that all or part of the discovery
requested may prevent a failure or delay of justice in the event of
further proceedings in the action in that court, it shall make an
order authorizing that discovery.  The order shall identify any
witness whose deposition may be taken, and any documents, things, or
places that may be inspected, and any person whose physical or mental
condition may be examined.  Any authorized depositions, inspections,
and physical and mental examinations shall then be conducted in
accordance with the provisions of this article relating to these
methods of discovery in a pending action.
   (f) If a deposition to perpetuate testimony has been taken under
the provisions of this section, it may be used in any later
proceeding in accordance with subdivision (u) of Section 2025.