Earlier in March, Musk said he would put the deal "temporarily on hold", while he waits for the social media company to provide data on the proportion of its fake accounts.
"Musk believes Twitter is transparently refusing to comply with its obligations under the merger agreement, which is causing further suspicion that the company is withholding the requested data," according to the letter.
A self proclaimed free-speech absolutist, Musk has questioned the accuracy of Twitter's public filings about spam accounts representing less than 5 per cent of its user base, claiming they must be at least 20 per cent.
Musk said he needed the data to conduct his own analysis of Twitter users and did not believe in the company's "lax testing methodologies."
"Musk is clearly entitled to the requested data to enable him to prepare for transitioning Twitter's business to his ownership and to facilitate his transaction financing," his lawyers said in the letter.
Musk has said that he has lined up financing for the deal, through equity and loans, pulling in top shareholders including Saudi Arabian investor Prince Alwaleed bin Talal and Sequoia Capital.
Twitter shares were down 5.5 per cent at $37.95 in early trading.
Twitter did not immediately respond to a request for comment.