Yes, in many cases. Since federal law and state law contain overlapping provisions, someone bringing a discrimination claim may sometimes pursue protections under both. For example, the federal employment non-discrimination law, called Title VII, applies to employers with at least 15 employees and forbids employment discrimination based on race, sex, age, religion, and disability (which includes HIV status).
While Title VII does not expressly forbid discrimination based on sexual orientation or gender identity, a growing number of courts and government agencies have taken the position that its proscription against sex discrimination encompasses both (See, e.g., United States & Dr. Rachel Tudor v. Southeastern Oklahoma State University, 2015 U.S. Dist. LEXIS 89547 (2015) (denying motion to dismiss professor’s Title VII complaint that school had subjected her to a hostile work environment based on her gender identity)). In two separate decisions in 2012 and 2016, the EEOC itself concluded that sexual orientation discrimination, gender identity discrimination, and sex discrimination are one and the same, since the latter two are based on preferences, assumptions, expectations, stereotypes, and norms associated with masculinity and femininity (See Macy v. Holder, EEOC Appeal No. 0120120821 (Apr. 20, 2012); Baldwin v. Foxx, EEOC Appeal No. 0120133080 (July 15, 2015)). Although the EEOC’s decisions are not binding on the courts, many have used similar reasoning in affirming Title VII’s applicability to discrimination based on gender identity and sexual orientation (See, e.g., Smith v. City of Salem, 378 F.3d 566 (6th Cir. 2004) (holding that Title VII prohibits discrimination against transgender people based on gender stereotyping); Videckis v. Pepperdine Univ., 150 F. Supp. 3d 1151, 1160 (C.D. Cal. 2015) (holding “sexual orientation discrimination is a form of sex or gender discrimination”)).
LGBT people who are discriminated against in housing may also be able to file a complaint with the federal Department of Housing and Urban Development (HUD) in addition to CHRO. For more information go to: https://portal.hud.gov/hudportal/HUD?src=/program_offices/fair_housing_equal_opp/LGBT_Housing_Discrimination.