The insulting online messages on Monday referenced Halsey's battle with throat cancer in 2009.
Halsey made two contentious decisions in United's 2-1 victory at Anfield on Sunday that went in favour of the visitors.
Liverpool midfielder Jonjo Shelvey was sent off in the first half for a challenge on Jonny Evans, and United was later awarded a penalty kick that was scored by Robin van Persie.
Halsey returned to refereeing in March 2010 following his cancer battle.
No Premier League referees have Twitter accounts, according to the body that oversees match officials in England.Suggest a correction