If the police do a proper investigation and determine there is probable cause that you committed the crime you will be charged. Your best defense is the security camera's in the store to show it was not you there during the alleged theft. I would also put together as much information as possible to show where you were during the commission of the crime. Before you speak to the police contact an attorney.
While these things always vary based on the facts, I can tell you generally, the police can arrest you when they have probable cause. Whether that probable cause comes from the officer's assessment or a warrant, depends on the situation. If the police believe they have probable cause and arrest you, you can make them prove that probable cause to a judge later, typically at a motions hearing. If the judge finds probable cause and that evidence obtained was done so in a legal manner, among other things, then the DA will have to prove that you did the crime beyond a reasonable doubt. Therefore, short answer - yes you can be charged. You claim of their mistaken identity would be a defense to the charge, but not an absolute bar to being charged.
The investigation by the police and accusation are perfectly legal. If you were truly a victim of identity theft that would be a defense at trial. Do not try to talk your way out of this. Refuse to answer questions and let a lawyer do the talking.
You need to consult a local attorney to help you sort this out. The Municipal Court Prosecutors in Colorado Springs are very competent and generally very fair to deal with. But, I advise you to retain an attorney to help you through this.
Best of luck to you.
Do not talk to the police or anyone else about the facts of the case other than a lawyer. If the police think you are guilty, they will not care what you have to say and might even mix something up to your detriment. If they feel they have evidence, they will normally charge you. It would be a good idea to get a lawyer fast to get evidence that will help you and possibly convince the police not to charge you.