AS THE granddaughter of Mother Maybelle Carter, the daughter of June Carter and the stepdaughter of Johnny Cash, Carlene Carter is heir to one of the richest traditions in country music. Yet it's her connection to stepsister Rosanne Cash that's most obvious on the new Carlene Carter album, "I Fell in Love."

Like Cash, Carter brings enough assertive rock 'n' roll to both her music and her lyrics to remove any suggestion of the fatalistic female victim in her country songs, yet she still retains the well-crafted songwriting and personal singing of traditional country music. The result is one of the most likable country-rock albums of the year.

Between 1978 and 1983, Carter put out four fine new-wave country albums (plus a fifth in Britain) that were critical favorites and commercial flops. Now, with the success of Lyle Lovett, k.d. lang and Rodney Crowell, the times have caught up with her, and "I Fell in Love" should be a country hit.

It certainly deserves to be, for the picking enjoys a loose, lively rockabilly swing, and Carter sings with the friendly accessibility of Kathy Mattea or Paulette Carlson. Carter's mom joins the harmonies on a fresh remake of the old Carter Family tune, "My Dixie Darlin'," and David Lindley plays fiddle and banjo on "Me and the Wildwood Rose," Carter's own memoir about her childhood days as a member of the Carter Family.

These songs effectively establish her roots, but more typical of the album is the first single, "I Fell in Love," which she co-wrote with two of Tom Petty's Heartbreakers, Benmont Tench and her producer Howie Epstein. With Albert Lee playing chicken-squawk rockabilly guitar and with harmony vocals from Levon Helm and Dave Edmunds, Carter belts out the song with the loose abandon of someone who has in fact fallen in love and just doesn't care about anything else.

Carter wrote or co-wrote nine of the album's 11 songs, and several of them (especially the unbowed good-bye song, "Goodnight Dallas," and the sassy, wild-woman song, "One Love") should be hits for someone else if they don't become hits for Carter.