The Glasgow North MP had been under investigation over claims dating back to 2016.
Last week the Metropolitan Police confirmed the sexual assault allegation was made on 22 June and submitted online by a third party.
The Glasgow North MP, who is now sitting as an independent, was suspended from parliament for two days after he was found to have made a sexual advance to a teenage SNP member of staff. After it was recommended that Mr Grady was suspended from parliament for two days, it emerged that Mr Blackford had subsequently urged his party's MPs to "give as much support as possible" to the MP when audio of an SNP group meeting was leaked to the Daily Mail.
In response, Mr Blackford said he was willing to meet the victim, adding: "If the complainant feels aggrieved, then I am sorry for that." If Mr Grady remains on the outside, then it will effectively spell the end of his Westminster career, with candidate selection for the next general election expected soon.
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