Ref Craig Langton is said to have tweeted to Charlotte Hennessy whose father, Jimmy, died in the tragedy.
Ninety-six supporters died during the 1989 FA Cup final in Sheffield.
A "public apology" from Langton, who is a fireman, was issued by his local Fire Brigade Union.
However, Hennessy says she hasn't received an apology after making the complaint herself.
Nottinghamshire Fire and Rescue Service say they were conducting an internal investigation.
One thing I can not STAND is liars. Absolutely no apology has been passed on to me or None at all!!
— Charl JFT96 Hennessy (@charlhennessy1)