Learn English – Can an inanimate object “claim” to do something? Like a car that “claims” 45 mpg

The word "whose" is used in several different grammatical ways. For some of these (see my original answer below), it has been grammatical to use it for inanimate objects, at least since the days of Shakespeare. For others (see my update), it is only used for people or animals.

ORIGINAL ANSWER:

Many people seem to believe that you cannot use whose for inanimate objects, but I don't believe this was ever proscribed except by out-of-control grammarians. Consider the following quotes from Shakespeare (selected from many more quotes where whose refers to an inanimate object) and more recent authors:

Hamlet I.v

I could a tale unfold whose lightest word
Would harrow up thy soul, freeze thy young blood,

Two Gentlemen of Verona, III.ii

By wailful sonnets, whose composed rhymes
Should be full-fraught with serviceable vows.

Timon of Athens IV.iii

The sea's a thief, whose liquid surge resolves
The moon into salt tears:

Jane Austen also used whose to refer to inanimate objects:

Pride and Prejudice (1813)

On reaching the house, they were shown through the hall into the saloon, whose northern aspect rendered it delightful for summer.

Also F. Scott Fitzgerald:

The Great Gatsby (1925)

I walked out the back way ... and ran for a huge black knotted tree whose massed leaves made a fabric against the rain.

Not to mention Pat Conroy:

South of Broad (2010)

... as I walk down Church Street, whose palmetto trees are rattling and whose oaks shake with the ancient grief of storm.

UPDATE: I just realized that whose is used in several different grammatical ways. In some of these ways, I would never use whose for anything but a person or animal. In particular, one of whose's uses is as an interrogative pronoun, as in:

Whose shoes are these?
Whose are these shoes?

If you had some leaves, and were asking which tree they fell off of, you cannot say:

*Whose leaves are these?
*Whose are these leaves?

You have to say something like

Which tree's leaves are these?

But when it is a relative pronoun that immediately follows its antecedant, whose can be used for inanimate objects:

The tree whose leaves look like hands ....

This may be part of the cause of the confusion about whether whose can only be used for people or animals.