Reductio ad absurdum, in this case used to express disbelief at the actions of the attending officers. We have the OP, who has from information given, had her house pulled apart after a complaint by a disgruntled neighbour whose cat appears to have died (likely of underlying causes, but certainly through no fault of the OP) on OPs premises. She seemed to take it as mockery of her, which was not at all my intention, and I hope she’s less shaken now.
Apparently the attending officers, even after OP explained that there had been heated messages sent by the aggrieved complainant on the same day, and after seeing physical evidence of a dead animal, conducted a thorough search for ANOTHER corpse. On the face of it, this doesn’t actually sound like something the police would ordinarily do, no, because even if there’s a report of a dead body in a house, the police are not necessarily ‘going to look for it.’
This is because there are limited circumstances in which they can search. It’s unlikely but not impossible that they could have obtained a warrant given the timescale. Another PP asked what the warrant said, this is because had they obtained a warrant they would have had to have a reasonable apprehension a crime had been committed - this apprehension would depend on the evidence provided to them. Who the hell knows what NdN said, maybe she said OP is Cruella De Ville, but what we DO know is that there was evidence presented to the police by the OP when they attended the address, ie. accusatory texts about a dead cat sent by the complainant on the same afternoon. There was also a dead cat, which the OP could prove had caused her distress and which she had tried to re-unite with its people.
This might well have indicated that an officer should re-interview the neighbour before deciding on whether or not to conduct a search, which as the OP has said, is disruptive and invasive. The disposal of any other at-this-point hypothetical body could have been prevented by placing officers in the house rather than pulling it apart.
In the absence of a warrant, even if the homeowner agreed to a search, there has to be an apprehension that a crime has been committed. Here, there had been a disclosure from the homeowner which raised a question of whether the initial complaint was vexatious. Such complaints are not unheard of and could absolutely have led the officer to determine there were insufficient grounds for a search, either with or without a warrant, without further investigation.
However nice they were to OP, professional judgement does come into play. The police do have a duty to investigate complaints, yes, but they are bound by procedures which must be followed, and be applied proportionately, as PPs have already explained.
Of course, the OP was innocent, shocked shitless and most people are understandably reluctant to argue with the cops.
I don’t see how this helps the OP, as what is done is done, but I won’t bother offering a critique on your post, given that you already know everything!