If I do a background check on my boyfriend, can he find out it was me that did the back ground check on him?

I smell something fishy with my boyfriend. Something is off. His stories aren't adding up. My family members would tell me his stories weren't adding up but I didn't want to believe them. Until I caught him in a lie but he didn't even notice that he told me the truth. I tried making up a story to get the truth out of him but it didn't seem to work. For a peace of mind I would like to do a background check on him. Can he find out I did a background check on him?
If I do a background check on my boyfriend, can he find out it was me that did the back ground check on him?
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