The US has a three pronged contribution to Euclid.  NASA is providing the near infrared detectors and associated electronics for the NISP instrument, NASA is participating in the Euclid Science Ground Segment (the processing of the Euclid photometric and spectroscopic data) via the Euclid NASA Science Center at IPAC (ENSCI), and a number of US scientists are helping to develop the tools and algorithms that Euclid will use to unlock the mysteries of dark matter and dark energy.  The US science participation in Euclid is primarily through three competitively-selected, NASA funded science investigations. These selected science investigations are: Precision Studies of Galaxy Growth and Cosmology Enabled Through a Physical Model for Nebular Emission (PI R. Chary, Caltech), Looking at Infrared Background Radiation Anisotropies with Euclid (PI A. Kashlinsky, GSFC), and Constraining Dark Energy and Gravity with Euclid (PI J. Rhodes, JPL). In addition, there are several US based scientists who are EC members but are not associated with one of these investigations. 
Euclid-US Science Teams:

The total number of EC members in the US is 107 (including 3 Euclid Founders and 7 Euclid Builders). They are:

Graeme Addison, Johns Hopkins University

Anahita Alavi (Caltech/IPAC)

Steven Allen, Stanford University

Philip Appleton, California Institute of Technology (IPAC)

Richard Arendt, NASA Goddard Space Flight Center

Matthew Ashby, Smithsonian Astrophysical Observatory

Micaela Bagley, University of Texas at Austin 

Sharan Banagiri, University of Minnesota

Rachel Bean, Cornell University

Giampaolo Benevento, Johns Hopkins University

Charles Bennett, Johns Hopkins University

Gary Bernstein, University of Pennsylvania

Alejandro Borlaff, NASA AMES & ESA

Mark Brodwin, University of Missouri at Kansas City

Volker Bromm, University of Texas at Austin

Sean Bruton, University of Minnesota 

Joyce Byun (University of Arizona)

Victoria Calafut, Cornell University

Daniela Calzetti, University Of Massachusetts, Amherst

Peter Capak, Oculus/Facebook (Euclid Founder)

Nico Cappelluti, University of Miami

Caitlin Casey, University of Texas at Austin

Ken Chambers, Univ. of Hawaii

Ranga Ram Chary, California Institute of Technology /IPAC

Yi-Kuan Chiang, Ohio State University

Hyung Cho, Jet Propulsion Laboratory

Judith Cohen, California Institute of Technology

Ami Choi, Ohio State University

James Colbert, California Institute of Technology /IPAC

Asantha Cooray, U California at Irvine

Behnam Darvish, California Institute of Technology /IPAC

Olivier Dore, Jet Propulsion Laboratory

Peter Eisenhardt, Jet Propulsion Laboratory

Daniel Eisenstein, Harvard University

Steve Finkelstein, University of Texas at Austin 

Jonathan Gardner, NASA Goddard Space Flight Center

Anthony Gonzalez, University of Florida

Shoubenah Hemmati, California Institute of Technology /IPAC

Christopher Hirata, Ohio State University 

Shirley Ho, Carnegie Mellon University

Warren Holmes, Jet Propulsion Laboratory (Euclid Builder)

Eric Huff, Jet Propulsion Laboratory

Albert Izard, Jet Propulsion Laboratory

Jeff Jacobson, California Institute of Technology /IPAC

Bhuvnesh Jain, University of Pennsylvania

Murzy Jhabvala, Goddard Space Flight Center

Stephanie Juneau, NOAO

Steven Kahn, Stanford University

Arun Kannawadi, Princeton University

Alexander Kashlinsky, NASA Goddard Space Flight Center

Alina Kiessling, Jet Propulsion Laboratory (Euclid Builder)

Alex Kim, Lawrence Berkeley National Laboratory

Jeff Kruk, NASA Goddard Space Flight Center

Bomee Lee, California Institute of Technology /IPAC 

Michael Levi, Lawrence Berkeley National Laboratory

Eric Linder, University of California at Berkeley

Xiang Liu, California Institute of Technology /IPAC

Robert Lupton, Princeton University

Eugene Magnier, University of Hawaii

Rachel Mandelbaum, Carnegie Mellon University

Dida Markovic, Jet Propulsion Laboratory (Euclid Builder)

Phil Marshall, SLAC

Daniel Masters, California Institute of Technology /IPAC (Euclid Builder)

Conor McPartland, University of California at Riverside 

Vihang Mehta, University of Minnesota

Brice Menard, Johns Hopkins University  

Bahram Mobasher, University of California, Riverside

Patrick Morris, California Institute of Technology /IPAC

Leonidas Moustakas, Jet Propulsion Laboratory

Peter Nugent, Lawrence Berkeley National Laboratory

Nikhil Padmanabhan, Yale University

John Palmieri, California Institute of Technology /IPAC

Matthew Penny, Louisiana State University

Saul Perlmutter, University of California, Berkeley

Alice Pisani, Princeton University

Steve Pravdo, Jet Propulsion Laboratory

Jason Rhodes, Jet Propulsion Laboratory (Euclid Founder)

Allan Runkle, Jet Propulsion Laboratory

Ben Rusholme, California Institute of Technology /IPAC

Ripon Saha, University of Missouri at Kansas City

Lado Samushia, Kansas State University

David Sanders, University of Hawaii

Jeremy Sakstein, University of Pennsylvania

Claudia Scarlata, University of Minnesota

David Schlegel, Lawrence Berkeley National Laboratory

Michael Seiffert, Jet Propulsion Laboratory (Euclid Builder)

Josh Speagle, Harvard University

David Spergel, Princeton University

Adam Stanford, University of California, Davis

Daniel Stern, Jet Propulsion Laboratory

Nathaniel Stickley, California Institute of Technology /IPAC

Michael Strauss, Princeton University

Istvan Szapudi, University of Hawaii

Peter Taylor, Jet Propulsion Laboratory

Harry Teplitz, California Institute of Technology /IPAC (Euclid Builder)

Georgios Valogiannis, Cornell University

Francisco Villaescusa-Navarro, Flatiron Institute 

Stefanie Wachter, Carnegie Observatories (Euclid Builder)

Augustyn Waczynski, NASA Goddard Space Flight Center

Yun Wang, California Institute of Technology /IPAC (Euclid Founder)

Risa Wechsler, Stanford University

Martin White, Lawrence Berkeley National Laboratory

Gerard Williger, University of Lousiville

Chris Wilson, Cornell University

Joan Xie, California Institute of Technology /IPAC

Kate Young, University of Minnesota

Lukas Zalesky, University of Hawaii