Why would an officer be trying to serve me papers that "were not signed by me" the night I was arrested for a DUI?

Absolutely you should talk to a criminal attorney.  They may be trying to get you to sign certain waivers, which they should've gotten you to sign before you were breathalyzed or questioned.  Politely refuse to sign, and ask them to speak directly to your lawyer.  Once they've been notified that you are represented by an attorney, they should cease interaction with you.  If they continue to approach you about this issue, talk to your attorney about it. 

Yes, things do sound a bit fishy.  If I were you I would go and see a criminal lawyer for consultation immediately on all of this.  What many people do not realize is that are many challenges that can be made to arrests that are improper and it is my understanding that DUI in Colorado is no exception to that rule. In other words, the police might have realized that what they did - or failed to do - is enough to challenge the arrest and have it thrown out (I am not saying that this is so I am just saying that maybe this is so).  So do NOT sign anything and tell the police that you have retained an attorney and to please refrain from coming by your home any more.  Good luck.