It's been a fairly miserable Thursday session for ASX shares so far today. At the time of writing, the S&P/ASX 200 Index (ASX: XJO) has slipped by 0.04% and is back under 8,140 points. But let's talk about what's going on with the ResMed Inc (ASX: RMD) share price.

Whilst the ASX 200 is having a bad day, it's been far worse for Resmed shares. This ASX 200 healthcare stock closed at $36.25 a share yesterday. But this morning, those same shares opened at just $35.30 and are now down a painful 3.5% at $34.98 each.

So why is the Resmed share price getting such a dramatic hammering this session?

What's up with the ResMed share price today?

Well, it's hard to know for sure. There haven't been any fresh developments or news out of Resmed itself today on the ASX.

But there are still a few things we can point out.

Firstly, it's been a pretty rough day for most ASX healthcare stocks. The healthcare sector is currently the third-worst performing sector on the markets, with the S&P/ASX 200 Health Care Index (ASX: XHJ) currently down 0.65%.

Other healthcare shares, such as CSL Ltd (ASX: CSL), Polynovo Ltd (ASX: PNV), and Cochlear Ltd (ASX: COH), are also suffering today.

Secondly, Resmed's US-listed stock also had a pretty bad night last night. Resmed has a dual-listed structure, meaning its shares can be found both on the Australian market and on the New York Stock Exchange. The American shares often set the tone for what happens on the ASX.

Last night, Resmed's American share price had a shocker, falling 5.12% to US$238.03 a share.

Our Fool colleagues over in the States posited that this fall might be a result of a broker downgrade. Wolfe Research's Mike Polark reportedly moved Resmed shares from a hold to a sell.

Resmed gets a sell rating

He also gave the company a 12-month share price target of US$180 per share, which, if accurate, would see the company lose a quarter of its value from current levels.

Polark's pessimism stems from concerns that Resmed might be poised to lose market share to its pharmaceutical rival Eli Lilly. He argued that "disruption risks to RMD's business rise in 2025-2026 due to Lilly's likely launch of an obstructive sleep apnea indication for its GLP-1 medication tirzepatide".

So that might have been what tanked Resmed's US stock last night, and thus indirectly responsible for today's poor ASX showing from the Resmed share price.

Despite today's sell-off, Resmed's ASX shares remain up a robust 37.7% in 2024 and 53.9% over the past 12 months.