Familysearch death index:
Name: Bertha Nelson
Burial Date: 19 Jun 1919
Burial Place: Brainard, Minn
Death Date: 18 Jun 1919
Death Place: Duluth, St. Louis, Minnesota
Age: 47
Birth Date: 06 Feb 1872
Birthplace: Denmark
Marital Status: Single
Father's Name: Nels Nelson
Father's Birthplace: Denmark
Mother's Name: Mary Erickson
Mother's Birthplace: Denmark
Informant: Magnus Peterson

     The remains of Miss Bertha Nelson, age 47, were sent from Duluth to Brainerd for burial. She died of lung trouble on June {blurry}. Short services were held at the Whitney chapel on Friday afternoon, with interment in Evergreen cemetery. Miss Nelson was a sister of the late Mrs. Charles Peterson residing in the country near Brainerd. (Brainerd Daily Dispatch, 20 June 1919, p. 2, c. 3)

The odd thing about all this is that Bertha's marker in the family lot of Charles and Anna Peterson has just "Aunt Bertha" - no last name or dates. Like she was a mystery to the family when the markers were put in (later?).

Charley J. Peterson m. Annie Catrice Nielson in Becker county on 22 Feb 1882

1885 MN census for Brainerd:
Family #961:
Johnson, John, 29, b. Sweden
Johnson, Josephine, 25, b. Sweden
Nelson, Hans, 23, b. Denmark
Nelson, Jennie, 20, b. Norway
Nelson, Erick, 27, b. Denmark
Nelson, Robert, 21, b. Denmark
Nelson, Bertha, 12, b. Denmark
Soranson, Mary, 52, b. Denmark
Family #964:
Peterson, Charles, 26, b. Denmark
Peterson, Annie K., 25, b. Denmark
(Christine 3, baby 30 days)
Peterson, Andrew, 27, b. Denmark

1895 MN census for Brainerd ward 4:
Family #66:
Peterson, Mike, 28, b. Denmark
Peterson, Annie, 27, b. Denmark
(Lillie 7, Gilford 5, Mirtel 2, all b. Minn.)
Family #67:
Nelson, Robert, 30, b. Denmark, res MN 14y E.D. 13y
Nelson, Bertha, 22, b. Denmark

1895 MN census for Twp 134 Rng 28, Crow Wing, MN:
Peterson, Chas, 35, b. Denmark, res. MN 13y E.D. 2y, Farmer
Peterson, Anna, 34, b. Denmark
(6 children ages 13 to 2)

1900 census for Brainerd ward 4 family #67:
Petersen, Mike, head, 33, b. Sep 1866 Denmark, m. 14y, imm. 1882
Peterson, Annie, wife, 31, b. Apr 1869 Denmark, 5 ch 4 liv, imm. 1886
(Lillie 12, Gelford 10, Myrtle 7, Ruth 2)
Nelson, Bertha, sis-in-law, 27, b. Feb 1873 Denmark, imm. 1886, dressmaker
(So is that a totally different Bertha?)

1900 census for Twp 134, Crow Wing, MN family #55:
Peterson, Charles, 41, b. Denmark, m. 18y, imm. 1881
Peterson, Anna, 40, b. Denmark, 8 ch. 8 liv., imm. 1881
(8 children ages 15 to 11/12)

(Anna wife of Charles died 12 Mar 1914.)

(Bertha Nelson died in Duluth 18 Jun 1919 - Magnus Peterson was the informant, and knew the names of Bertha's parents, who would be the same as for his wife, Anna, if Bertha and Anna were sisters.)

1920 census for Duluth Precinct 41, family #470:
Peterson, Magnus, head, 52, b. Denmark, imm. 1877
Peterson, Anna, wife, 51, b. Denmark, imm. 1884, nat. 1886
(Gelford 28, Alice 15)

So unless there happens to be two Bertha Nelsons, both born in February 1872/3, it sure looks like Bertha was the sister of Ann Peterson, wife of Magnus/Mike.