Chances of getting a Spouse visa if there is a check in police verification

[gurvinder_singh83]

Hi

My cousin is applying for a spouse visa for US. She had been in UK for some time, did her post graduation there and also worked for a couple of years.
For the purpose of spouse visa she initiated a Police background check in UK and they have provided the background check with a note in the letter saying
offence : unlawful immigration in EU member state on date ---
That happened because she overstayed for a few months in the UK.

Now my question is, if this remark can lead to her denial to spouse visa??
or if there can be any complications because of it?

Thanks