The Hispanic oversample changed in 2002 when the ASEC underwent a sample expansion that involved the addition of CPS households identified from prior samples in order to improve the precision of ASEC estimates for Hispanic households (the Hispanic oversample, first implemented in 1976) and uninsured children (the Children’s Health Insurance Program (CHIP) oversample, first implemented in 2001). While households included in the Hispanic oversample are identified based on their participation in prior November CPS samples, they are interviewed for the ASEC supplement in February or March, depending on their month in sample (MISH) in November. Similarly, households identified as part of the CHIP oversample, including non-Hispanic, non-White households identified based on their participation in prior August through November CPS samples are interviewed for the ASEC supplement in either February or April. In summary, all additional ASEC interviews (as of 2002) take place during the February-April period (read more here on the CPS Sample Design and about oversample selection and interview timing of the ASEC on p.19-20 of Technical Paper 77).
It is important to note that ASEC questions on health insurance coverage generally reference past year coverage rather than current coverage (this changed in 2019 when they added current coverage questions), and indicates if the person had that type of coverage at any point in the past year. For this reason, you may want to consider whether this data will be suitable to answer your research question about coverage in March. If, however, you want to use past year coverage with March as a starting point, you should use ASECOVERP to identify people in the ASEC Oversample. If you decide to exclude people in the oversample, I believe you will need to modify the weights using information available on p.23-25 of Technical Paper 77.