A newer article on U-Pb dating of carbonates by Troy Rasbury: Article Directly dating geologic events: UPb dating of carbonates
https://pubs.usgs.gov/pp/0474a/report.pdf This is an old, but very appropriate paper.
My paper on Uranium-lead dating of dolomite:
Luczaj, J. A. and Goldstein, R. H., 2000, Diagenesis of the Lower Permian Krider Member, southwest Kansas, U.S.A.: Fluid-inclusion, U-Pb, and fission-track evidence for reflux dolomitization during latest Permian time, Journal of Sedimentary Research, v. 70, p. 762-773.
I disagree with Ayob's statement that "U is not found in sedimentary rocks, especially no carbonate rocks unless it is in clays". Roll-front deposits, which are primarily in sandstones are certainly sedimentary rocks, and the U is NOT bound to clay in this type of deposit. There are direct U minerals in these deposits, such as uraninite. These sedimentary rock ore deposits are where we get most of our uranium!!
With regard to carbonate rocks, there are certainly U-enriched carbonate rocks. This is one of the applications of spectral gamma ray well logging. U-Pb dating of carbonates requires that the U be residing in the carbonate minerals themselves (not in clays). There is abundant literature on this for the past 20+ years. It might not be ore grade, but carbonate rocks CAN have elevated uranium (both limestones and dolomites). The Permian rocks of the Hugoton Embayment of southwestern Kansas USA), for example have uranium concentrations up to at least 30 ppm, and based on fission track analysis, it's the carbonates that are hosting the uranium. I can send you 2 references for this case study if you email me: luczaj 'at' uwgb.edu
Limestone-hosted U deposits play only a minor roll as far as U concentration in sediments is concerned, excluding the example from the Jurassic Todilto Limestone, USA (Hilpert and Moench 1960). The deposits in limestone have a somewhat similar mineral assemblage to that of the other deposits in the San Juan Basin containing V in tyuyamunite and carnotite and As in santafeite besides uraninite. But they are unique in the type of host rock. It is an epigenetic U deposits in carbonaceous limestones. Red hematite-bearing sandstone forms its footwall rocks („Entrada Sandstone“) with the primary source of U resting in the Fe-Mg silicates chlorite and biotite. Evaporative pumping of uraniferous ground water caused immigration into the carbonaceous and reducing environment of the Todilto Limestone which is representative of algal stromatolites. Uranium may have derived from a wide range of source rocks and source minerals. Often volcanic or volcaniclastic interbeds are rife with glass shards and labile volcaniclasts. Fe-Mg silicates chlorite, biotite and amphibole as well as accessory minerals (e.g. monazite, xenotime) may be considered as potential U sources, the latter, however, are very refractory and less susceptible to leaching than e.g. glass shards. It may be indigenous mineral grains or extrabasinal granitic, volcanic and metamorphic source rocks that may account for the U concentration in sandstone-hosted U deposits. A closer look at the various processes responsible for U concentration in sandstones shows chemical reduction of U 6+ and transformation into U 4+ as ground water of Eh > 0 moves into reservoir rocks of Eh < 0 or reducing gas (e.g. H2S-bearing) migrating into oxidizing near-surface waters is an important factor. Decrease in pH paralleled by a drop of CO3 2+ and SO4 2+ contents by ground water mixing or host rock reactions may also lead to a precipitation of U minerals. Evaporation along with increasing temperature and the resultant formation of anion complexes which combine with uranyl to insoluble compounds such as carnotite or francevillite can be a key factor in uranium accumulation in this site.
I hope I could give you an overview of this uncommon host rock of U.
The brightest example of U mineralisation in carbonate rocks is the TUMMALAPALLE producing district in India (Andhra Pradesh). The article that can help to know something about the district is: Goswami S., Bhagat S., Zakaulla S., Kumar S., Rai A.K. Role of organic matter in uranium mineralisation in Vempalle Dolostone; Cuddapah Basin, India // J. Geological Society of India, 2017, V.89, 2017, Pp.1-11