An investigation is under way into reported breaches of the Health Protection Regulations 2020.
On Thursday, 1 October, a Member of Parliament contacted Police Scotland to report she may have breached legislation and guidance relating to Covid-19.
This related to her actions earlier this week, including a train journey on Tuesday, 29 September, between London and Glasgow, following a positive Covid-19 test.
Following consultation with Police Scotland, officers from the Metropolitan Police, working with British Transport Police, are conducting an investigation into potential offences.
The Parliamentary Commissioner for Standards has been informed.