But their paths are never going to cross in Earth Prime-Time.
Both 'Backstrom' & 'Grimm' are part of Earth Prime-Time, but both shows have different agendas as well as being on different networks.
But we can make it more believable that they are never going to interact with each other.
Portland is a major city in Oregon; there's going to be several police precincts. Backstrom and Burkhardt are probably all the way across town from each other. And Backstrom's team is the Special Crimes Unit - they would handle high profile crimes like the Los Angeles 'Major Crimes' unit while Reynard's precinct handles any cases that are called into their squad.
But that doesn't mean there can't be some kind of unofficial crossover between the two shows.
The lead singer of the band Inescapable Truth was found dead after he escaped from rehab. The band was a large ensemble that built on shamanic totems, which included them all wearing animal masks which were supposed to represent their inner animal spirits. The murder victim, Sebastian Serafian, was "the lion", while his killer was "the eagle". Others were "the bear", "the raccoon", "the ram", etc.
But what if the band was subtly broadcasting their own "inescapable truth" with those totems?
What if they were all wesen, those human/animal hybrids that were the special province of Nick Burkhardt as the grimm who had the special power to hunt them down?
A leonine wesen would be of the "Lowen" classification. The murderer was probably a "Steinadler". As for the others, the band members must have included at least one "Jagerbahr" (the bear), a "Waschbahr' (the raccoon), and perhaps a "Ziegevolk" (the goat) acting as the ram substitute.
None of Backstrom's team would be aware of any of this. The secret of the wesen has been kept from Mankind for centuries. (And as long as it is kept under wraps, it won't affect the standing of 'Grimm' in the main Toobworld. Should it ever become common knowledge, the series would have to be removed to some alternate dimension just as was the case with 'Being Human' and 'True Blood'.)
And we weren't made privy to their being wesen because none of the band members woged. And there was no grimm on Backstrom's team through whose eyes we could have had a point of view.
However, I am partial to the idea that one of Backstrom's fellow cops might be a wesen - Dr. Nadia Pacquet. Something about her feels more foreign than just her accent.....