On Sunday, officers with the Houston Police Department found the man's body on the sidewalk near Buffalo Bayou Trail.
When police officers were looking for witnesses, they found the woman lying on a stairwell leading up to the intersection of Congress and Smith Streets from the trail.
The Houston Fire Department paramedics pronounced both victims dead at the scene. Investigators believe the man was in his 30s and the woman was in her 60s.
Authorities are working to find a motive and said they don't have a description of any suspects.
If you know anything about this case, authorities urge you to contact the Houston Police Department's Homicide Division at (713) 308-3600 or Crime Stoppers of Houston directly.
Information leading to the charging and/or arrest of any felony suspects may result in a cash payment of up to $5,000.
Tipsters must contact Crime Stoppers directly to remain anonymous and to be considered for a cash payment by calling 713-222-TIPS (8477), submitting an online tip, or through the Crime Stoppers mobile app.