The Clues: Okay, these were fairly obvious: the cat (Magenta) was scratching her neck a lot.
Almost continuously in fact.
This caused the second clue: a huge raw patch of skin, which developed into an open wound.
Because she was constantly itchy, she unfortunately spattered blood everywhere around the house (fun to clean off, let me tell you!) thus creating the "crime scene" effect.

(Incidentally, if you are cleaning your walls and floor of blood, this can be done with warm water, vinegar and a splash of tea tree.
Use your microfibre cloth on the walls and furniture, and the usual mop on the floor.
Soft furnishings I scrubbed with the same solution and the microfibre cloth too, using the scourer section of a sponge on the difficult bits) There was a slightly less obvious clue in the scabs that had formed around Magenta's neck (they were tiny, but many).

Eliminations: I knew this wasn't a flea allergy, because I treat all my animals for fleas and worms.
Personally I use Advocate.
I don't really like the idea of medicating my animals for no reason, but when you think about intestinal worms, heartworm and fleas, the Advocate really is the better option.
With cats, make sure you apply it to the back of their head, as they can easily reach the back of their neck and lick the stuff off, which is really not good for their health.
Actions: This particular incident went from "itchy cat" to "blood everywhere" in a very short space of time - just about a week, in fact.
So as soon as I noticed that Magenta was bleeding, and why, she was taken to the vet.

Don't mess around with your health of the health of your family - furry or human.
If concerned, seek professional medical assistance from your GP, naturopath or vet.
In the case of cats, as soon as you notice any symptoms, see your vet, as they can go from apparently healthy to very sick very quickly.

The vet verified that there were no fleas and took a scraping to check for mites.
There were no mites, so he suggested it could be a food allergy - apparently cats can develop an allergy to specific types of food or additives to their food, even if they've been successfully eating it for years.
This tends to present as scabs around the neck area, where Magenta had hers.
I bought the hypo-allergenic food recommended and gave it a go.
A month later and she had improved somewhat, but there was still a sore, and she was still scratching.
It got worse again towards the end of the month, so another vet visit was in order.
This time, to provide her with some temporary relief, she received a shot of cortisone.
This would hopefully give her some time for the itchiness to dissipate, because as we all know, skin itches while it's healing!! I got another bag of the hypo-allergenic food while I was there.

All this time, the other cats in the house, Tortuga and the two foster cats had not displayed any symptoms at all.
Magenta is not as robust as the others...

Once back at home, with Magenta sleeping and hopefully healing a bit, I frantically searched the net to try and find some solution - I didn't think the food was the issue, as the month hadn't helped much.
Finally I found a pet naturopath site, which recommended natural foods (which would be good, I'm sure, but would need a lot of variety to ensure they got all the necessary vitamins and things) and also clean, filtered water.
Mental face-palm!! This was my job! This is what I did, and I had overlooked it!! In my defence, we only have one of those bench-top filters (we're renting) and I do have a dog who drinks between five and ten litres of water a day (which is why we have to stop at every tree on the afternoon walk); plus all the other furries.
However, this looked like it could be a potential solution, so I filled the water bowl with filtered water.
All the animals seemed a lot happier, obviously they dislike the taste of chlorinated water as much as I do.
Also, within a week, Magenta's wound had almost closed, and she still wasn't scratching.
It's now been two weeks, Magenta's wound has closed, her fur has grown back and she looks normal again.
She doesn't scratch much at all and we no longer have blood spatter all over the house.
She also steals the other cats' food, so she's back on the "normal" food again, with no adverse effects.
All the animals seem happier drinking the nicer tasting water.
Conclusion: Chlorinated water causes dry, itchy skin and the related problems in animals as well as humans.
Make sure that your furry family all get nice clean, filtered water to drink.
It makes it a lot less frustrating when you can't find the cause of the illness.
I've been reminded not to take anything for granted, and to remember to apply my profession to my own house.
I'd welcome your comments and feedback...