LDS says he is "of Lancaster, PA." This is probably the Cornelius Bodine who married Angeline Carpenter. He is listed in 1850 Census of New Haven Township, Huron County, Ohio. Here is the data from that census (my thanks to Joan Best for sending me this info):
Cornelius Bodine, 31, male, farmer, $1875, NY.
Angeline Bodine, 24, female, NY
Jane Bodine, 5, female, OH
George, 3, male, OH
Mariah, 2, female, OH
This family is also listed in the 1880 Census of the same place. Here is that data:
Cornelius Bodine, 62, farmer, NY, PA, NY.
Angaline Bodine, 57, NY, CT, NY.
Jane E. Bodine, daughter, 35, single, OH, PA, NY.
Guy L. Bodine, son, 22, OH, farmer, PA, NY.
Allie B. Bodine, daughter-in-law, 23, OH, PA, OH.
There appears to be a mistake here since Cornelius says he is born NY, but his children say he is born PA. Maybe the transcription of the census is incorrect.
Ronny Bodine agrees that this Cornelius Bodine is the one who married Angeline Carpenter. Here are some notes he sent:
From 1850 through 1880, Cornelius Bodine was living with his family in New Haven, Huron County, Ohio engaged in farming. In 1860, he was called Chas. C. Bodine, then aged 42.