As far as I was able to find out, the short answer is NO. However, if you have paid all money owed in full, you may be able to convince the former landlord to file a voluntary dismissal of the case. Or if it was filed and you cured the reason for eviction, nonpayment for example, a case dismissal is appropriate.
If your eviction was dismissed; or you paid all money owed in full, you also may be able to have the eviction removed from your credit reports. Or if not removed, at least show that it was dismissed, or the debt satisfied.
I'm not a lawyer, please do not consider this as legal advice.