Her death certificate also might tell her parents names and/or birth place. She might have naturalization papers. Let us know if you have any of these.
Can you say more about Iver Madsen and Nels Hansen - date of birth, spouse, children, anything, everything? I didn't see Iver Madsen in Wheaton, Cass, North Dakota in a quick search on Ancestry. I saw more than one Nels Hansen from Denmark.
Most likely Chrestina's family knew Iver Madsen, or his wife, or were related to them. Her relationship to him/her could be key to identifying Chrestina in Denmark.
Here's an Iver Madsen coming from Vordingborg...
1871 EMIGRATION registration in Copenhagen Name: Iver Madsen Occupation: Landmand Age: 32 Contract # 145400 Forevisningsdato: 5/8/1871 Birth place: ? Sidste oph.sogn: Vordingborg, Præstø Destination: Faribault, Minnesota, USA Ship's name: indirect route, no ship name given Bemærkninger: BST: Minn påført med anden håndskrift. IDkode: I7172M030
It would be fun to get to the bottom of this mystery!