modal perfect?

Hello, I would like to ask a question about the following situation:

In a story, a letter had been stolen and the police was looking for it. Now, is my question: (Where was it? Asking about possible hiding places for the letter, in the past)

Where could the letter possibly be? (It could be in the drawer)

or

Where could the letter have been? (It could have been in the drawer)

thank you

I’m assuming that this is part of the narrative rather than a piece of dialogue. This is a stylistic choice, and for the author to decide. “Where could the letter possibly be?” places the reader more vividly at the time at which the question arose.

I assume also that your question is about the difference between “be” and “have been”, and that the omission of “possibly” in the second sentence is irrelevant or accidental.

yes, it is just to stress it is a possibility question

I understand that the question in the present can be: Where is it? Where can it be? Where could it be? But I would like to ask a question using a past reference (Which places were possible?). According to my knowledge, could is used in the past as the past form of can only for a general ability…however, could have been´s definition is “it was possible but didn´t happen”. I cannot work out the correct form out of these definitions…

You’re right that “could have been” is often used for “possible but didn’t happen” cases, but it can also be used for “don’t know” cases like “Where could it have been?”

My most natural reading of “Where could the letter possibly be?” in a past-tense narrative (and not in dialogue) is that it is a present-tense interruption – a sort of aside from the author to the reader – designed, as I mentioned, to place the reader more vividly at the scene (though less vividly than “Where can the letter possibly be?”, which might seem too much of a “shock”). In this context I suppose it may also be possible to read “Where could the letter be?” as past tense, or as some ambiguous fusion of past and present. This is quite a subtle point.