What areas of our property can police search
when there is a warrant for a person living at
this address?
The answer depends on the nature of the warrant and its scope. WIthout reviewing the warrant, the answer is not an easy one. In most cases, the warrant would include the tenant's habitable area and any common areas.
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The question is not very specific. Assuming the "warrant for a person" is an arrest warrant, not a search warrant; then presumably the scope of the search would be limited to places the person could be hiding (as opposed to inside a small box, etc.), and perhaps areas near persons present for weapons. But - much would depend upon the specifics in the case.