As long as the authorities have what they consider to be appropriate evidence (whether video, eyewitness, or whatever) they can charge you with the crime. Of course, whether you get convicted or not is another matter.
I am sorry. Sometimes the additional information furnished only shows up after we answer.
First of all, I hope you have not given a statement, nor said anything to the police or anyone about this. DO NOT talk to them unless you have a lawyer present. In a criminal case, the prosecution has to prove "beyond a reasonable doubt" that you did the crime they are accusing you of. You don't have to prove anything.
Through your lawyer, make them show the video. Cross examine the store officer. How does he know that just because you were pulling away, that you were the one in the store? Were there other cars around? Do you go to the store often? Sometimes people are "recognized" and picked out because they have been seen in the store at other times.
But, again I will say that they do not need to see you in person stealing shoes to charge you or convict you, if the evidence is enough. I am sure you have seen the "police" shows on TV where they show the video of someone robbing a bank and ask if anyone has seen that person. If they catch him, the video alone will probably not convict, but it will help. In your case, the video and the testimony of the store office might be enough to charge you with theft. I don't know what else they have to convict you. Fingerprints on the old shoes? Proof that they were yours? New shoes and tags in your car? Maybe they have nothing.
Your best defense is to just make them prove their case.
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