Well, in general, a search requires “probable cause.” A dead body lying on the ground would usually qualify as probable cause for a search of the immediate vicinity – but what is “the immediate vicinity”? A 3-10 ft radius around the body? The next room? The whole building? The courtyard outside the building?
You specifically said “search the property” which implies other rooms (or apartments) and associated land and structures (yards, toolsheds, etc) – all these would be considered one property… However, it is very common for all these to be subject to any one person’s consent. A landlord or building superintendent can give you access to search many areas of a property, but s/he does not have the right to search a tenant’s apartment at will, and can’t therefore assign that authority or right to you.
Homicide detectives would of course investigate all directly accessible and visible areas as much as possible without violating the privacy, ownership or access rights of others. They should be a bit cautious about extending the boundaries of the search, lest any evidence --and evidence derived by use of that initial evidence be thrown out (as “fruit of a poisonous tree”).
As you describe the case, asking a judge to grant a warrant is simply basic prudence. If you can’t convince a judge now that you ahve a good reason to search a given area, you’re likely to have difficulty getting another judge to allow any evidence you gather on your own say-so, or evidence derived by using it. Also there are legitimate questions: does merely living or doing business in a building where a person was murdered make me enough of a suspect to warrant a violation of my right to provacy?
You might go for a warrant if a landlord or tenant (including commercial tenants, like many bars) refuses to grant permission for a search on your terms. You might also go directly for a warrant, without asking permission for a more immediate search, in many cases. If, for example, a tenant grants you permission to search their apartment, and you find a lockbox, you can’t force it open. They have to open it or grant you permission to force it, because owning a lockbox isn’t “probable cause” for any crime–it may be for love letters, their kid’s lemonade stand, storing toy rocket engines, etc. If a tenant asks you to leave the apartment, you must.
Since voluntary permission might suddenly end if you find the first hint of anything interesting, and since any imminent evidence (guns, drugs, bloody clothes) might disappear before you returned with a warrant, you may choose to simply explain the situation to a judge, and get a warrant that doesn’t rely on the voluntary (revocable) cooperation of any private citizen (potential suspect or accessory)
Getting a warrant isn’t a big deal. You just explain your reasons to a judge, who will consider some of the objections/laws a defense lawyer will bring up at trial. Except for the delay, it really benefits the police as much as all the many citizens that could be affected by blanket warrantless searches.
