Fitch Ratings finds the impact of lower crude oil prices will impact U.S. cities differently, though Houston may be a standout in terms of financial risk.

U.S. crude oil prices are down more than 50 percent from this time last year. An increase in oil production, largely from reserve areas like the Eagle Ford shale basin in Texas, has pushed markets toward the supply side.

Fitch found that, since at least the early 1980s, local government finances have been linked strongly to energy prices. Using metrics like tax revenue and gross domestic product, the ratings agency found some Texas cities in particular were pressured by the weak crude oil market.

For the state as a whole, tax collections for June were down 1.4 percent year-on-year, marking an end to a near five-year streak of gains.

"We believe cities like Houston are facing some risk due to the decline in oil," the ratings agency said. "Most major regional and multinational energy companies have offices in the Houston area, exposing it to employment pressures."

The Dallas Federal Reserve found the state as a whole added 35,800 net jobs in July for the largest monthly gain so far in 2015.

Keith Phillips, a senior economist with the bank, said the strength in the jobs market seen in July likely won't last.

"The decline in oil prices may dampen the momentum in job growth in the months ahead," he said in a statement.

The so-called Beige Book published by the Dallas Federal Reserve earlier this year said the low price for crude oil is hurting the state's oil sector. A research report from the bank in June found major economic concerns for the state were the low price of oil and the longevity of the depressed market.

Fitch said a city like Houston has few means to increase tax revenue. Several energy companies this year have announced staff reductions, leaving Houston feeling the brunt of the job market cuts.

"However, Houston's job diversity may mitigate some of this risk," it said. "Roughly 30,000 workers there are employed by hundreds of refining plants in the area, which benefit from lower oil prices."