Not being a policeman it's not my job to say how an investigation should be done. I would suggest taking statements from man and any witnesses, establishing identities, looking at evidence at the scene, making a judgement if statements are coherent and are corroborated by evidence. If not arrest suspect, otherwise continue investigation until sure no crime has been committed.
I take it your approach would be to march in, arrest the man and tell him it's for his own good as he now gets a free lawyer. Like I said, subtlety isn't your strong point is it?
Some simple things are, how would you investigate, where would you conduct the interviews, would you bring separate say, caravans to the site so you can both have somewhere to put the "suspects" to question them, and hold them while you also question other suspects, just so you don't have to arrest them?
Legally, for the person being arrested it is BETTER they be arrested than asked to come of their own accord down to the station. They will have FAR more legal rights arrested than not.
To conduct the investigation you rightly suggest take place, you need the forensics guys to come in, do you think they walk in, talk a pic, walk out and discuss it outside and instantly come up with an answer? no, likewise police get called out, detectives get called out, maybe their boss gets called out. What does the potential murderer do all this time, they just sit him in the back of a squad car and ask him politely not to run off?
First thing you do, detain any suspects, its really pretty simple, you investigate, you interview, investigate more, and interview again.
You need to generally speaking, get a look at the crime scene, speak with everyone involved who you can, compare stories to any quick evidence you have, then re-interview, compare stories, doing so will in most cases give you a massively, massively better idea of the situation than you will minutes after you arrive at a crime scene. So yes, decisions like releasing people or keeping them further should be made later on with a heck of a lot more information then right after it happened guessing at who was right or wrong.
Detaining suspects is the ONLY sensible option we have. What if it turned out to be flat out murder but because you can't detain anyone unless you're sure of their guilt, he fled the country.
There are some awful stories of stupid cases that get handled wrongly or seemingly have the wrong and very unfair verdict, but just as many situations like these turn out pretty well for the homeowners.
Yeah, he sounds like the kinda guy you want in possession of a lethal weapon 