Sexual violence victim charities have slammed the supposed clip, which is claimed to show men encouraging sexual violence.
While the original video is believed to have been pulled down, or even not to have existed at all, Devon and Cornwall Police are investigating allegations that an encrypted Whatsapp group has been set up to promote the idea in the UK.
A spokesperson for the force said: “Police have received a report of the existence of the WhatsApp group and are currently making enquiries regarding the credibility of the group.”
Falmouth University in Cornwall has also said it is investigating social media posts appearing to encourage the "abhorrent" day.
A spokesperson for the university said: “We have become aware of a number of messages and social media posts circulating in relation to an abhorrent TikTok ‘24 April Hoax’ encouraging sexual violence.
"There is no evidence that reports of these posts and purported related discussions are genuine, or that there is a genuine threat, but it is clear that the issue is causing distress to our community and we therefore want to make clear that we are taking this issue seriously."
They added: "We are actively working with the police to support their investigations and the university will take a zero-tolerance approach to anyone found participating in any related group chats, whether private or public, or engaging with the content in a way that could reasonably be foreseen to cause distress or emotional harm, whether intended or not.
"We would strongly encourage anyone with information about individuals engaged in any such discussions to come forward and support the university, to ensure our campus remains a safe and inclusive environment and so that enquires can be progressed.”
The police stressed that most of social media claims around the day came from abroad - and it was not localised to Cornwall or the UK.
It comes as women in the US urge others to stay indoors after rumours of the stomach-churning threats for April 24 were released on the popular video sharing app.
Meanwhile, one campaigner described the idea of a 'National Rape Day' - where laws are suspended and rape is legal - as "abhorrent".
Katie Russell, from Rape Crisis England & Wales, told The Sun Online: "Our understanding is that this disturbing so-called ‘trend’ on TikTok began as a hoax, and no evidence has been found of the original video threatening a national day of sexual violence in the USA.
"Regardless of its origins, or whether or not it was intended as a ‘joke’ at any point, the very concept of such a day is abhorrent and has caused many people, particularly women and girls, a great deal of understandable fear.
"The ‘trend’ will no doubt have also been extremely distressing for many, not least of all victims and survivors of rape and all forms of sexual violence and abuse who might have had vivid memories and flashbacks to past experiences triggered by this."
She added: "Obviously, despite one particular piece of misinformation that has featured in this so-called ‘trend’, there is no day or moment where laws are suspended and rape is legal in the USA or anywhere else in the world.
"Rape and sexual assault are always serious crimes.
"It should also go without saying that rape and all forms of sexual violence and abuse are traumatic experiences that can and do have wide-ranging and long-lasting impacts, and are never appropriate topics to ‘joke’ about."
Andrea Simon, director of End Violence Against Women Coalition said: "Regardless of whether this is a hoax or not, we know the use of threats of sexual violence and derogatory comments about women’s appearance and bodies are very common forms of online abuse that women are subjected to.
"We wouldn't accept threats to rape offline and we can't ignore them online. They intend to intimidate and silence women in online spaces, causing real harm to individuals and to society and should never be tolerated."