Andy Murray has been subjected to online abuse after declaring his support for the Yes campaign in the independence referendum.
The Scot had previously remained silent on the issue but posted a message on Twitter just hours ahead of the polls opening, to state his position.
He tweeted: "Huge day for Scotland today! no campaign negativity last few days totally swayed my view on it. excited to see the outcome. lets do this!"
But his comments were met with abuse on the social media site.
Someone calling himself Harry S who tweets as @sportingharry wrote: "Wish u had been killed at Dunblane, you miserable anti-British hypocritical little git. Your life will be a misery from now on."
Other users of the social media site were quick to condemn Harry S's comments, with one tweeting: "you're more of a disgrace to Britain than Murray ever will be" and another describing him as a "right horrible human being".
Police said they are monitoring social media.
Assistant Chief Constable Bernard Higgins said: "People who put abuse such as this online should be utterly ashamed of themselves for making such vile, disgusting and distasteful comments.
"We are monitoring social media and where appropriate will take action against those involved.
"Social media is important for many people but it must be used responsibly. There is no place for personal abuse of any kind on it."
Murray is the latest in a string of celebrities to be targeted online over their stance on the independence referendum.
Famous people who have urged Scots to stay in the UK - such as David Bowie and JK Rowling - have found themselves the subject of online abuse from pro-independence supporters.
The 2013 Wimbledon champion has been quizzed on the issue previously but dodged the question, although in an interview in June he did criticise Scottish First Minister Alex Salmond for waving the country's flag at the tournament last year.
Murray will not have a vote as he is not currently resident in Scotland. In 2006, he courted controversy when he said he would support "anyone but England" in the World Cup.
Last month he told the Guardian that he did not think it looked likely the result would be a Yes, but he added that his preference would be to represent Scotland if the country became independent.
"If Scotland became independent, then I imagine I would be playing for Scotland," he told the newspaper.
"I haven't thought that much about that yet because I don't think it's looking too likely that it's going to happen.
"But if it did happen, then it would be pretty much the first time in my life that I would have ever (had the chance to play for Scotland)."
He added that he did not like making his views on politics known as previous comments had "caused me a headache ... and a lot of abuse".