It's a bit of a grey area where some people are saying that an RT-PCR is needed, some are saying it's only for symptomatic patients. I'd recommend you get your test done regardless to stay on the safer side.
Lastly I went to Uttarakhand in oct and if you are vaccinated then RTPCR is not needed. Although at checkpoints they will ask for epass which I filled in front of officers and it hardly took 5 mins. There you need to upload your vaccination certificate. Hope this may help you.