Lurking for years but now need some reasoned advice please. I am a department manager with an assistant department manager I inherited when I joined the company, and a team underneath us. I am trying to not to divulge anything identifying so please bear with me. The assistant department manager has been massively underperforming without improvement so I was having to take more and more steps to manage this, which didn't go down well with him. He has been off on long term sick for months with depression. While off he has been telling the rest of the team he does not like me and I am the reason he is off. I have done absolutely nothing to warrant this and I have the full confidence of my managers and HR.
However, my managers and HR are reluctant to take this further due to him suffering with depression. I'm not upset or hurt by the comments because I know I have none absolutely nothing wrong and he is just hiding from/deflecting his problems. But I am angry he could treat me this way. All my managers have done is have a face to face meeting as part of his long term sick management and said, we know this has happened, it's not appropriate/professional/etc and here is a reminder of the conduct policy. I didn't admit or deny it but just sat in silence.
WWYD? Should I make a formal complaint? I don't want to come across petty or cause him further distress. But I also think this is a serious issue that is totally unacceptable, and I am not sure depression justifies this. Obviously will never get an acknowledgement/apology from him as so much time has passed with him being off.