Does a Character or Pawn not always has an owning connection if...?

I have a character and from it I want to run a server RPC. But if I play the client I get this message in the output log:

LogNet: Warning: UNetDriver::ProcessRemoteFunction: No owning connection for actor BP_BBS_Character_C_1. Function SR_ApplyDamage will not be processed.

I run in editor with 2 Players, one listen server, one client. I thought that the character has automatically an owning connection.
The character is set through game mode and spawns at player start.
Could this be a bug?
Does a Character or Pawn not always has an owning connection if it is set in the GameMode and spawned through PlayerStart?

I found out. The Character has an owning connection. Problem was, that the Actor that triggers the RPC was not implemented right for multiplayer so now it works.

Characters do not have owning connection. Controllers do. The Game Mode create a controller for each connection. All characters are “Spawned”, then “Possessed” by a controller.