A man has been arrested after officers investigated a complaint of personal information being shared online with referee John Beaton and his family spending Thursday night at home under police protection.
A 19-year-old man was arrested in connection with a data protection offence and Police Scotland have confirmed enquiries are continuing.
It follows Beaton's decision to award a controversial penalty to Celtic at Motherwell on Wednesday evening after a VAR check.
Beaton judged Motherwell's Sam Nicholson had committed a handball when a long throw was launched into the box. Kelechi Iheanacho converted the subsequent penalty in the 100th minute to give Celtic a 3-2 win at Fir Park and put them a point behind Scottish Premiership leaders Hearts going into Saturday's title-decider at Celtic Park, live on Your Site.
"Scottish FA condemns in the strongest possible terms attempts to compromise the safety of match officials," a statement said.
"Such vigilantism, motivated by decisions perceived to be right or wrong on a field of play, is a scourge on our national game and we are grateful to Police Scotland for their swift intervention.
"We are also clear, sadly, that this is the inevitable consequence of the heightening criticism, intolerance and scapegoating demonstrated this season by media pundits, supporters, official supporters' groups, clubs, players, managers and former match officials.
"We do not make that point lightly as the national association. Yet it is an inconvenient truth. Those who have sought to apportion blame and conspiracy towards match officials to deflect from defeats or perceived injustices throughout the season have contributed to an environment that puts the safety of our staff and match officials in jeopardy.
"This is the consequence of a hysterical media narrative, fuelled by irresponsible knee-jerk post-match media interviews, commentary and official social media posts. The cumulative effect impacts on our ability to provide enough referees to service our game at all levels. When it compromises the safety and wellbeing of our most senior match officials, enough is enough.
"Referees are not infallible. Mistakes will be made on the field, and subjective calls made in front of the VAR monitor, just as managers will pick the wrong team, goalkeepers concede soft goals and strikers miss from five yards out. Yet the reaction to these inevitabilities could not be more contrasting.
"What happened yesterday is not an isolated incident. There are many examples of match officials being placed in harmful situations but with individuals fearful of speaking out lest it exacerbates the situation or causes further alarm to friends, family and colleagues.
"We will not allow this to become the norm. We will not allow a situation where match officials require special provision to protect their children at school to be considered an occupational hazard.
"We will not allow a situation where staying at home with the front door locked and avoiding the hazards of public interaction becomes a coping strategy.
"The Scottish FA will be seeking to strengthen its rules to better protect those integral to the game and urge those who will doubtless join us in condemning incidents like this to support those proposals, not contribute to their watering-down on the basis of self-preservation.
"As we approach what should be an exciting finale to the season, we ask those who have personalised and hyperbolised their opinions, those who have sought the easy way out by attributing defeats to perceived refereeing errors, and those who have approved incendiary statements and posts to reflect on their contribution to creating an environment of intimidation, fear and alarm.
"We urge tolerance and perspective to prevent any further, unthinkable escalation."
