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Automatic denials of applications are eviction records, rent judgments, or negative rental history and criminal records that include drug dealing, violent and sexual crimes, theft and arson*.  All income must be verified. Most owners require 2 to 3 times the monthly rent in income.  1-2 full years of residency will be verified.  Money orders or cleared checks showing payment of rent is required(Unless the unit is priced below $650 studio/1 bedroom or owner demands different) 

Yet according to FAIR HOUSING you have the RIGHT to apply regardless of owners rental criteria. *More info