He was arrested, for suspicion of whatever offence he was alleged to have committed, interviewed and then bailed on police bail, whilst the police conduct their enquires, who at the end of their enquiries, present their findIngs to the CPS, who then decide if their is enough evidence for a realistic chance of a conviction or not.
This can and does sometimes take a long time.
Defamation etc are civil matters not criminal.
If the complaint was found to
be vexatious or malicious, the complainant could then be arrested for perverting the course of justice etc.