Hmm... Let's see if I get this straight...
You kill someone in a gunfight (technically murder or manslaughter, possibly in self-defence as a mitigating circumstance).
You call cops.
Cops don't believe your story and fine you the full whack.
Cops claim there were no witnesses WHO BACK UP YOUR VERSION OF EVENTS... how do YOU know there were or weren't any either? Did you tell them about any witnesses? Did you mention any names of other people involved, or people who might have seen the event your way? If you didn't, and the police have not had any calls reporting the incident and your innocence in it, then they are perfectly within their rights to say that they had no witnesses - because nobody else has come forward to defend you, and you haven't provided any!
The cops are allowed to RP whether they believe your story. If your story sounds flaky, or if the reasons given for the initial cause of the firefight implicated you in any crime or 'suspicious' circumstance, then they may well decide they already have a 'downer' on you and your story. If you then also can't provide any witnesses or supporting evidence, or if they think you might simply be trying to (literally) get away with murder, then they have every right to slam you in jail for it (or ticket you, as they did in this case - bear in mind that NORMALLY, murder is a guaranteed jail sentence, so maybe they already cut you a bit of slack here, but you didn't realise).
As for the 'crime-logger' - you're presumably talking about the Wanted List... which is pretty much the core of the system that tracks (most) serious crime. At least, those crimes that can be detected by the game-engine (usually those involving a death or a robbery). As such, the 'game' is the witness. It is the little old lady across the street who saw the incident, and provided a description (which matches you quite accurately - the cops don't actually KNOW your name, until they've challenged you, despite the glowing white banner above your head). Or the game is the innocent bystander in the coffee-shop; the bartender; the shopkeeper; the woman who was pruning her roses in a nearby garden; whatever. It's enough to 'report' the crime, and give sufficient description to the cops HQ, who then plonks your name on an All Points Bulletin-type thing, so that all cops who encounter you, will give chase (for example, if your car goes whizzing by and your name pops up as vehicle-owner on their ANPR systems), or will run a routine check on you when quizzing you on foot.
There is of course an element of 'meta-gaming', but this should be downplayed by the cops, and treated as a report of the incident itself - without interpretation - in essence 'bloke fitting your description (for whatever reason) was reported as killing another person in manner X'. Beyond that, it's down to you to convincingly claim that you had a good reason, or were acting honestly, etc. Sometimes, if your RP is 'shifty' or your story doesn't quite hold water, or even if the cop is just having a bad day and doesn't have time to piss about, he'll opt not to believe your cock-and-bull story, and will just bang you in the clink, or whatever. This is, sadly for you, perfectly acceptable. Maybe next time, grovel a bit more? Or RP a better story? Or ask to speak to superior (as pleasantly or politely as you can). You'd be amazed at the number of times someone kills another person and then gets all shirty with the cops (who've had to track him down, rather than him handing himself in), because they ask for more detail. He'll get all 'fuckthepolice' and 'Iknowmyrights' with them, and start insulting them or whining and resisting restraint (usually because he's got an illegal weapon or some other dodgy whatnot in his bag, etc, or just because he's a tit). And then he's surprised when the cops don't believe his story about how the victim 'jumped out in front of me' or 'was trying to steal my illegal rifle that I was using to rob people with'.
Bear in mind the cops have heard it *all* before. And then some. So occasionally, you just have to accept that their discretion is quite powerful... and be prepared to kiss some ass, if you want to get let off for what is *technically* still a crime, even if you didn't mean to do it. Convincing the cops in those situations is *everything*... and some people really don't get that. On Altis, they are practically judge, jury, and executioner (almost)... so a little humility can sometimes go a long way!