Do single crossovers occur in circular polynucleotides?
Although crossover events can be observed in mitosis (mitotic recombination), they most frequently occur in prophase I of meiosis (crossing over in bivalents). Circular chromosomes are common in prokaryotes, but eukaryotes have linear chromosomes. Remember what meiosis accomplishes and that prokaryotes reproduce asexually. Prokaryotes don't have a need for -- or engage in -- meiotic division, so crossover events in circular chromosomes can really only be observed in instances of mitotic recombination, and I don't know the frequency of this in prokaryotes. 

In prokaryote DNA replication, if any entangling of the two product circular chromosomes occurs, it is resolved by DNA topoisomerase. So perhaps a crossover would present a similar situation and the cell would resolve it by similar means.