The subpoena asks that the results of Patterson's polygraph taken shortly after the disappearance of Lubbock State School workers Kay Harrelson and Peggy Merimon.
Patterson is the main suspect in Merimon's disappearance and Harrelson's murder.
The subpoena is part of the civil suit the women's families have filed.
Patterson's lawyers say in their motion that the results are protected because the man who gave the test, William Teigen, is a former employee of their's and those results are guarded under attorney-client privileges.
Patterson's family has also made a motion that they not be made to give testimony in the civil proceedings.
Patterson's lawyers had no comment on the case.