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Did they do a serum test?

The tests on the blood stains on the Shroud have been tested far more than just a simple serum test. Two of the world's top experts on Blood, Blood fractions and blood descendant compounds did extensive work on the blood stains. The Late Drs. John Heller and the Late Dr. Alan Adler

Heller and Adler (hereafter H&A) concluded that it was actual blood material on the basis of physics-based and chemistry- based testing, most tests of which will be discussed, specifically the following:

detection of higher-than- elsewhere levels of iron in ‘blood’ areas via X-ray fluorescence,
indicative spectra obtained by microspectrophotometry,
generation with chemicals and ultraviolet light of characteristic porphyrin fluorescence,
positive tests for hemochromagen using hydrazine,
positive tests for cyanmethemoglobin using a neutralized cyanide solution,
positive tests for the bile pigment bilirubin,
positive tests for protein,
use of proteolytic enzymes on ‘blood’ material, leaving no residues.
The tests and data not discussed are the

reflection spectra indicative of bilirubin’s32 and blood’s presence,33
chemical detection of the specific protein albumin,34
the presence of serum halos around various ‘blood’ marks when viewed under ultraviolet light,35
the immunological determination that the ‘blood’ is of primate origin,36
the forensic judgement that the various blood and wound marks appear extremely realistic.37

After isolating old methemoglobin from sample from the Shroud, after already proving it was blood, they wanted a second opinion. The called Dr. Bruce Cameron, who holds a double doctorate specialized in hemoglobin in all its forms. They submitted their findings to him. . .

Upon returning to the New England Institute, Heller ran in and seized Adler. After the coordinates had been plotted on graph paper, Adler observed, “John, this is hemoglobin. It’s the acid methemoglobin form, and it’s denatured and very old.” Heller “beamed” before noting, “But Al. We don’t have the requisite fine structure,” to which Adler replied, “Fine structure, my foot! Do you think this is the spectrum of sauteed artichoke hearts? Don’t be ridiculous.” Suggested Heller, “Let’s check with at least two other top hemoglobin hotshots and see if they are as sure as we are. Pick anyone you want.” Adler’s choice gave the answer of old acid methemoglobin. They then spoke via speakerphone to Bruce Cameron, “whose double -doctorate is dedicated to hemoglobin in all its many forms,” and upon receiving and plotting the numbers, Cameron said, “You both should know what it is. It’s old acid methemoglobin. I don’t know why you wanted to bother me with something you know as well as I do... Hey, wait a minute. Are you two idiots working on the Shroud of Turin?” At this point, Heller and Adler shook hands after smiling at each other.108 The Shroud of Turin’s ‘Blood’ Images: Blood, or Paint? A History of Science Inquiry
David Ford — University of Maryland Baltimore County—10 December 2000

In the mid 2000s to 2012, more immunological studies have been done on the blood from the Shroud and it has been proved to have been Primate blood. . . but is it human?

These studies confirmed that among the anthropoid apes, only orangutans and gibbons express both A and B antigens, similar to humans. Chimpanzees do not express the B antigen and gorillas lack the A molecule (75). Thus, forward typing studies would effectively exclude all nonhuman primates as a possible source of red blood cell membrane AB antigens on the Shroud, except for possibly gibbons and orangutans. In addition to ABO molecules, approximately thirty other blood group antigens are expressed on the surfaces of human red blood cells. One such group of blood molecules, the M,N, and S antigens, has been examined on blood- stained Shroud fibers using immuno- histochemistry methods. MN antigens are found on red blood cells of all anthropoid apes, but the S antigen is only expressed in humans (76). Bloodstained fibers were positive for expression of M, N, and most importantly, S antigens, ruling out a contribution of (nonhuman) primate blood (77). Blood on the Shroud of Turin: An Immunological Review — ©2012 Kelly P. Kearse

If you really want to read some dense biological science, the the link that block quote above was cut from will keep you occupied, and perhaps in a dense cloud of scientific prose for a long time. . . but it is very interesting.

Essentially, the immunological study of the blood shows that the stains on the Shroud are human blood.

No amount of obfuscation and denial from the skeptical community's non-specialists who raise questions of egg Albumin and tempera paints that sound erudite in non-peer reviewed popular press can even approach the peer-reviewed work done by these scientists published in qualified scientific journals and replicated by experts working IN their fields.