I have heard this idiom being used in the negative sense on TV to express annoyance when someone is too meticulous.
However, from what I remember, it is a positive trait to have, i.e., to be thorough and detail oriented with your task.
Can it be used in the negative sense as well?
Most dictionaries of idioms that I've checked do not give space to any negative element that may lurk at the extreme end of "dotting your i's and crossing your t's." Here, for example, is the entry for the expression in Cambridge International Dictionary of Idioms (1998):
dot the/your i's and cross the/your t's informal to do something very carefully and in a lot of detail | She writes highly accurate reports – she always dots her i's and crosses her t's.
From John Ayto, Oxford Dictionary of English Idioms, third edition (2009):
dot the i's and cross the t's ensure that all the details are correct. informal
From The Wordsworth Dictionary of Idioms (1995):
dot one's i's and cross one's t's to take great care over details: She makes a good organizer because she is always careful to dot her i's and cross her t's.
From Longman Dictionary of English Idioms (1969):
dot one's/the i's cross one's/the t's not fml to be very careful to thorough: pay great attention to small details: you'll have to make sure you dot your i's and cross your t's if you go to work at that company: they're very keen on details.
And from Christine Ammer, The American Heritage Dictionary of Idioms, second edition (2013):
dot the i's and cross the t's Be meticulous and precise, fill in all the particulars, as in Laura had dotted all the i's and crossed all the t's, so she wondered what she'd done wrong. This expression presumably began as an admonition to schoolchildren to write carefully and is sometimes shortened. William Makepeace Thackeray had it in a magazine article (Scribner's Magazine, 1849): "I have ... dotted the i's." {Mid-1800s}
Obviously, if you are characterizing a lawyer, an editor, or an accountant as someone who dots all the i's and crosses all the t's, it is difficult to take that description as a criticism, except perhaps indirectly as regards the person's likelihood of being a bon vivant or sparkling conversationalist.
Nevertheless, it is possible to take by-the-book carefulness too far—in some walks of life, anyway. That penumbrally negative aspect of the expression rises to the notice of A.P. Cowie, R. Mackin & I.R. McCaig, Oxford Dictionary of Current Idiomatic English, volume 2: Phrase, Clause & Sentence Idioms (1983):
dot the i's (and cross the t's) be meticulously correct in what one does or says; make clear in every detail something which may be obvious or well understood already | There are many i's to dot and t's to cross before we can feel certain about the exact relationships described here in in broad detail. [H. J. Eysenck, Sense and Nonsense in Psychology (1957)] | The shares may not break through the chart barrier at around their current 42p until full-year figures are produced, dotting the i's, but then they should move smartly ahead. [The Sunday Times (1967–83)] | The novelist's own belief had been that the scandal lay, not in the political field, but in an indefinable, though very definite, impression of sexual indiscretion of the unnecessary crossing and dotting of the t's and i's, which were perfectly well known, but not to be advertised. [Angus Wilson, Hemlock and After (1952)] | 'I see you've got my point,' the lawyer continued. 'There's no need for me to dot the i's and cross the t's then.' | usu in order of headphrase.
The expression may therefore be appropriate in some situations where a person's punctiliousness shades into obsessive and/or unnecessary exactitude.
