Detective Matthew Miller said the two incidents occurred in the 700 block of West Fannin Street, and he said it is possible that the same person committed both thefts.
The first incident involved the burglary of a residence during which someone stole a 72-inch television on April 17.
The next incident involved a vehicle burglary on April 18. That time the thief got away with $700 in cash.
Anyone who might be able to provide enough information to result in an arrest could qualify for a reward of up to $1,000 from the Coastal Bend Crimes Stoppers organization.
Persons who provide information on crimes always remain anonymous.
Anyone who might know something about the two crimes can contact the organization by calling 362-0206. Anyone living out of town may contact the organization toll-free at (877) 362-0206.
Internet users may get in touch with the organization by emailing the information they have to coastalbendcrimestoppers.com.