In 2013, a federal judge said Apple violated antitrust law by colluding with book publishers to raise e-book prices above Amazon's standard $9.99 pricing for digital books, after the publishers settled.
The attorneys general, who were both involved in the e-books price-fixing investigation, appear to be pre-emptively looking into the terms of Apple's new music service for any signs of industry collusion before Apple Music is available to consumers at the end of this month.
Unlike Spotify and other streaming music services, Apple does not offer a free version of Apple Music. But the company offers a three-month free trial period and says it will let artists and record companies make various kinds of content, including songs and videos, available for free on Connect, a promotional section of its service.
Read MoreApple Music is a 'giant nothing burger': O'Leary
The so-called freemium model used by services like Spotify has been at issue over the last year.
Last fall, the singer Taylor Swift removed her music from Spotify in a dispute over its free version, In recent months top executives at the major record labels have been sharply critical of free services, arguing that they do not generate enough money and they give consumers no incentive to pay for music.
Yet Spotify, which started in 2008, has been by far the fastest-growing subscription music service, with 60 million users, 15 million of whom pay. Last year, the company had $1.3 billion in revenue, and 91 percent of that money came from subscriptions. However, Spotify, which is privately held, also reported a net loss of $197 million.
But some artists and executives at independent labels have defended the freemium model.
Last month, Stephen Cooper, the chief executive of the Warner Music Group, the smallest of the three majors, warned that "before people conclude that freemium should be burnt at the stake, we should think very carefully about the consequences."