No, but it cost you more
Utility companies don’t report to the credit bureaus, so your late bill payment won’t appear on your credit report.
If you default on your utility bill and it is sent collection, the collection agency would report the defaulted debt to the credit bureaus and then it will show up on your file.
Paying your utility bills a month late is not impacting your credit report or score, but it may negatively affect your record with the utility company. If you keep doing that for a long time, they may disconnect you and require a deposit before reconnecting you back. Not to mention that you are paying more because of late fees.
My advice – find a way to get current and stay current.