Authorities piecing together the life of a deceased man suspected of killing at least six women and children — including his toddler daughter — want to learn about a woman he was seen with in the 1970s, saying she may be the toddler's mother.

Terry Peder Rasmussen, who died in a California prison in 2010, used multiple names in numerous states. Authorities believe his victims included an unnamed woman and three girls whose bodies were found in barrels near a New Hampshire state park in 1985 and 2000 and that he may be the father of one of the girls.

Rasmussen lived in Phoenix in the late 1950s and early 1960s, for part of 1969 and then in 1973, authorities said. He was married and had three daughters and a son.

The Maricopa County Sheriff's Office arrested him on April 30, 1973, as a fugitive from justice. Authorities on Thursday released a booking photo from that time, hoping people may recognize him and help account for his whereabouts in the mid- and late-1970s.

Rasmussen was arrested again in Phoenix in June 1975 on an aggravated assault charge. It's believed that his wife and children left him shortly afterward.

Authorities say Rasmussen was last seen by his family in Payson, Arizona, around Christmas of 1975 or 1976. He was in the company of an unidentified woman. He indicated he was living in an apartment complex in Ingleside, Texas, at the time.

"Authorities remain very interested in identifying the unknown female who was with Mr. Rasmussen during that visit, as she may be the mother of Mr. Rasmussen's daughter who was found murdered in Allenstown," New Hampshire Attorney General Gordon MacDonald said in a statement released Thursday.

Authorities know little about Rasmussen's whereabouts from that time to 1978 but say it's likely he spent time in Texas, Arizona, California, Oregon, Virginia and New Hampshire.

In 1985, a hunter discovered the first two bodies near the Allenstown, New Hampshire, park — the woman and a girl believed to be 9 or 10. In 2000, an investigator found the other two girls — one believed to be 2 or 3 and the other 3 or 4.

They believe the woman is likely the mother of the eldest and youngest girls. DNA tests show Rasmussen fathered the middle girl. The time of their killings was narrowed to 1980 to 1984.