If I'm renting from a private owner in a mobile home park and the park wants to do a background check on me, can they since I'm not renting from them?

Question Details:

I want to know if this is something that I have to do or is it unnecessary? We are renting from a private owner of a mobile home and was given paperwork from the mobile park to fill out and it included a sheet to sign for a background check. I do not feel comfortable giving them my SSN.

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