Local Search probably has more ranking signals involved than regular keyword search, because details such as geographic proximity, presence in business directories and listings in data aggregators' data sets, existence of phone numbers and local addresses, among other factors influence local search.
In Google Maps, there are strong indications that backlinks are weighing in less strongly. Additional ranking factors appear to be playing into the mix such as what we call "citations" or "references" whereby businesses, their sites and locations can be referred to without a hyperlink.
For instance, if a distinctive business name is mentioned in text, or its address, or its phone number -- these other signals can be used by the search engine as indications of relative popularity.
In addition, one could mention a website in an article without linking the domain name URL - this could also be a reference citation.
As evidence of this, one can find cases in Google Maps where business listings which do not have associated websites are ranking higher than some listings which do have websites. Since a business with no website cannot really have hyperlinks pointing to it, Google is obviously using a mixture of other ranking signals which it deams to be stronger than backlinks to determine ranking.
The original Google PageRank algorithm was based upon evaluating the number of backlinks and each of their originating pages' relative weighting to determine any given page's rank value. This method was inspired in large part from Google PageRank inventors, Brin and Page, observing how relative numbers of citations for academic and scientific research papers could be used to determine which papers were the most important. Research papers that were widely cited by other research papers must be more important than those with fewer citations. Applying this theory to the internet, Page & Brin observed that hyperlinks were a form of citing of pages on the internet, and the PageRank algorithm was born.
Some subsequent Google patent filings show that Google has come up with other types of information which could be used as relative reference citations.
The apparent influence of citations in rankings has caused some in local search marketing such as David Mihm to declare that "Citation is the New Link".
So, yes, backlinks influence ranking in local search, but it seems clear that in addition to links, other forms of citation may be equal or stronger ranking factors.