Fran Allison, 81, the Human Side Of 'Kukla, Fran and Ollie' Show

Fran Allison, the warm-voiced human component of the popular television show ''Kukla, Fran and Ollie,'' died of bone marrow failure at the Sherman Oaks (Calif.) Community Hospital yesterday. She was 81 years old and lived in Van Nuys, Calif.

To a generation of children in the late 1940's and the 50's, Miss Allison was the girlfriend, mother and gentle conscience of the Kuklapolitan Players, the puppet troupe created by Burr Tillstrom. Thanks to Tillstrom and Miss Allison, who treated the puppets like people, their exploits and personalities made them family favorites on prime-time television for 10 years.

''I adored Kukla and Ollie - they were never anything but real to me,'' Miss Allison said in an interview. Joining the Kuklapolitans She was born in La Porte City, Iowa, and after graduating from Coe College became a teacher. Later, she auditioned as a singer on a local radio station. By 1937, she was a popular radio personality in Chicago.

In 1947, she joined the Kuklapolitan Players, and they made their television debut the following year. ''I needed a girl who could talk to a dragon,'' Tillstrom explained.

By 1950, the show had six million viewers. As Fran, Miss Allison seemed particularly fond of Ollie, an outrageous, single-toothed dragon who adored buttered popcorn and putting his hair in curlers. Kukla loved to lean on Ollie's head, messing his hair. Fran was the soothing character.

In those years, television was performed live and Miss Allison once admitted she never knew in advance exactly what the puppets would say. ''On the air, you say exactly the same thing you would say if it happened for the first time, off the air,'' she said in an interview. A Baritone Dragon

In the early 1950's, Miss Allison made her Town Hall debut, assisting Ollie, whose full name was Oliver J. Dragon, in his first Manhattan performance as a baritone.

''It may be ironic,'' The New York Times observed in 1952, ''but Kukla and Ollie still seem so real that it's always a little disturbing when Burr Tillstrom steps into view.''

When the program went off the air, it left a group of sad adults and children. ''One of the most imaginative shows ever developed in the electronic medium,'' wrote the Times critic. The program reappeared briefly in the 1970's. Burr Tillstrom died in 1985 at the age of 68.

In the 1960's, Miss Allison was host of a show of films for children and appeared in musicals on television. In Los Angeles, she was host of a program for the elderly, ''Prime Time,'' on KHJ-TV.

Miss Allison is survived by her brother, Lynn, of Chicago.