Moyse who is the director of the Media Monitoring Project Zimbabwe (MMPZ) had presented himself to Gwanda police on Wednesday weeks after he was briefly detained in Harare over the same charges.
He was ordered to return the following day in the company of his lawyers.
His lawyer Kossum Ncube of the Zimbabwe Lawyers for Human Rights said police recorded a warned and cautioned statement from Moyse.
Ncube said the police said he would be summoned if they need him to help with investigations.
When he was initially arrested on December 6, police seized documents, DVDs and videos at the MMPZ headquarters where they were allegedly looking for material related to the Gukurahundi atrocities in Matabeleland.
Police had also detained three MMPZ monitors, Fadzai December, Molly Chimbanda and Gilbert Mabusa in Gwanda on charges that they distributed subversive material during a public meeting.
They were granted US$50 bail each by Gwanda magistrate Douglas Zvenyika
But the three spent seven days at Gwanda Prison after the State invoked section 121 which suspends bail pending an appeal to the High Court.
They were only released by Bulawayo High Court Judge, Justice Nicholas Mathonsi after he dismissed the appeal by the Attorney General’s office.