If the man were part of the store's loss prevention team and has you on tape stealing something he can make a citizen's arrest. The fact that he didn't leads me to believe he's playing games with you. The police can come to your home upon a complaint and some evidence to support an arrest but most shoplifting cases result in an arrest on the spot. You would have been held by store security until the police arrived. This man sounds like a wack job.
I agree with the previous answer. Grocery stores usually do not have full-time professional security people. This sounds like a manager or employee playing detective. It suspect that he was trying to identify an unknown person seen on a security tape and thought you were the person. Such tapes are not very good quality and it could be someone else who looks like you. Don't shop there anymore.
If you are visited by the police, I suggest you inquire politely why they are there and if they tell you that they are investigating a potential shop lifting, ask them where and when the incident took place and whether you are the target of the investigation. If you get the wrong answer, tell them politely that you would like to have a lawyer sit in on the matter. You may be able to make an appointmrnt to go to the station.
When the incident is in the past and the merchansise is not recovered, it is very unlikely that the evidence is sufficient to bring a prosecution. I lawyer will have an easier time finding out about the evidence than you will representing yourself and may even be able to see the tape before you are questioned. You will have a tendency to say too much.