When the guard shows up, that is the arrest. You should have had to speak to Aureus to get him arrested. You can head to the jail, downstairs in the legion headquarters, but I don't think Roberts will speak to you there.
You do not need to break into any houses or back rooms to advance the quest (or pickpocket, if you are adverse to that, as well). If you explore outside of town (still on the Cyseal map), you will eventually find evidence to point to the murderer.
What is illogical about an investigator (witch hunter) in a medieval setting, in a time of war, not necessarily respecting private property rights? It's not like there is a judicial system in place to request a search warrant...
That said, some people do have trouble with this quest line, possibly due to trying to follow it linearly, rather than exploring Cyseal and keeping an eye out for leads (or not paying attention to character comments after visiting the crime scene, etc). There is also an alternate solution if a character has Pet Pal (though it still requires collecting physical evidence).
