The assignment (at the residential burglary site in North Dallas) took most of the morning and would not have allowed White to get to Dealey Plaza in time. However, that is not to say that White was done working for the day once the assignment in North Dallas finished.
Here is a quote from JFK and the End of America book:
"White was not a real cop, but he was paid city employee in training to be a cop. So he had access to a police uniform, but he was not officially on assignment that day (11/22/63)."
Further down on the same page of a book there is a description that Beverly Oliver saw White on a grassy knol wearing uniform. So many misleading clues about White.