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No, unfortunately not. If you had full coverage insurance they will usually cover the cost of the impound fees but there is no law that would allow a recovery against the police.
Many people are under the impression they should be able to sue the police for not letting them know when the vehicle was impounded. However, the courts have ruled for years that the police can't be sued for not doing their jobs.
I'll give you a couple of case cites that stand for this proposition.
Castle Rock v. Gonzalez, 545 US 748 (2005).
You can read an article on it at http://www.nytimes.com/2005/06/28/politics/justices-rule-police-do-not-have-a-constitutional-duty-to-protect-someone.html and at https://en.wikipedia.org/wiki/Town_of_Castle_Rock_v._Gonzales
The actual case can be read at https://www.law.cornell.edu/supct/html/04-278.ZS.html
There is another case that was from the DC Court of Appeals called Warren v. District of Columbia which you can read about at https://en.wikipedia.org/wiki/Warren_v._District_of_Columbia and the actual case is at https://scholar.google.com/scholar_case?case=9108468254125174344&q=warren-v-district-of-columbia&hl=en&as_sdt=2006
Please remember that when reading case law the facts are never going to be the same as with your case, you have to look for the legal principles involved.