Yes, there's some alien hunting going on.
Well, yes, money is being spent to search for intelligent aliens. The obvious case is SETI, the Search for ExtraTerrestrial Intelligence. Quoting from their mission statement,
Our mission is to explore, understand, and explain the origin and nature of life in the universe, and to apply the knowledge gained to inspire and guide present and future generations. We have a passion for discovery, and for sharing knowledge as scientific ambassadors to the public, the press, and the government.
In their FAQ, they give more information:
The Institute has suites of activities in three arenas: (1) Astrobiology, the efforts to find and understand the prevalence of life in general (for example, microbial life under the parched landscapes of Mars or the icy crust of the jovian moon, Europa); (2) SETI, experiments designed to detect radio or light signals that would reveal the presence of technically sophisticated beings; and (3) Education and outreach projects that inform the public about our research, encourage young people to become more proficient in science, and train teachers in so-called STEM subject areas.
The important part there is (2): Detection.
In terms of financial status, they are a 501(c)3 non-profit organization. They are, of course, fond of donations from people and corporations. So yes, they are spending money.
The Arecibo Observatory is another famous player in the extraterrestrial contact arena. Their description of themselves is
The Arecibo Observatory is part of the National Astronomy and Ionosphere Center (NAIC), a national research center operated by SRI International, USRA and UMET, under a cooperative agreement with the National Science Foundation (NSF). The NSF is an independent federal agency whose aim is to promote scientific and engineering progress in the United States. NSF funds research and education in most fields of science and engineering. Additional support is provided by the National Aeronautics and Space Administration (NASA)
The radio telescope there has famously sent some messages. The most famous of these was the Arecibo Message in 1974, towards M13, a globular cluster.