The company has released three iterations of its smart ring to date.
It tracks metrics like heart-rate variability, blood oxygen rate and sleep patterns.
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Ultrahuman did not respond to requests for comment on the allegations.
The company has also yet to respond to the allegations contained in the legal filing.
Oura alleges that Ultrahuman gained access to proprietary information about its ring technology through former employees.

No coincidence?
Oura claimed that the similarities are not a mere coincidence.
The Finnish company goes as far as to claim Ultrahuman imitated its social media content for promoting the gear.

Oura is seeking damages of amount to be proved at trial.
The case could initiate a lengthy legal battle between two of the wearable industrys most significant startups.
Whats at stake?
Both companies have attracted a sizable amount of venture capital funding.
Its other investors include Temasek, MSD Capital and Salesforce boss Marc Benioff.
Oura appointed a new chief executive last year in Tom Hale.
That covers a wide range of products from smart watches to trackers like FitBit.
Smart rings are a relatively smaller subset of that market.
It now boasts over one million devices sold and celebrity users like Jennifer Aniston and Kim Kardashian.
It has also rolled out a subscription service, bringing the company into the SaaS arena.
Meanwhile, Oura has deepened its investment in R&D.
Earlier this year, Oura acquired San Francisco-based digital ID startup Proxy, which specialises in encrypting sensitive data.
This hinted at a much bigger vision for Oura and its wearable gear.
Ultrahuman has its own vision too.
Much like Oura, it too operates a subscription service.
Oura is seeking a jury trial.
Ultrahuman has yet to respond in the Texas court but will in all likelihood do so soon.
At that stage, the case will take greater shape but both sides could be facing a lengthy process.