From "The Tell-Tale Heart," how would I write a police report about the discovery from the perspective of the policeman on the scene?
To write a fictional police report about discovering the murder in "The Tell-Tale Heart," you should focus on the diction and style of a police report given in the U.S. in the 1840s. This might be difficult, as many of these records have been destroyed and others are not available to the public. However, you can mimic this style by looking at the general writing style of the time, artificially making it "less educated" (as police officers were not typically well-versed in grammar and spelling), and using a specifically formal mode of address, focusing on descriptions and details rather than flowery prose.
I foamed --I raved --I swore! I swung the chair upon which I had been sitting, and grated it upon the boards, but the noise arose over all and continually increased. It grew louder --louder --louder! And still the men chatted pleasantly, and smiled.
(Poe, "The Tell-Tale Heart," xroads.virginia.edu)
The above-scene would be good to focus on, as it is the part of the visit where the police become aware that something is wrong. With the initial report of a shout dealt with, the police remained to chat with the narrator, who must seem manic and over-confident. As his mental state degrades, the police will -- having instincts about criminal behavior -- decided to remain on the premises to see what will happen. The report would culminate with the discovery of the body and the narrator's arrest; it should be mentioned that details should be flat and expressionless, not over-emotional.