From The Modern Phrenology Department:

Erin White of The Wall Street Journal warns prospective employees they may be probed.

Rodney Archer, a 51-year-old engineering consultant in Silicon Valley, had spent several hours interviewing for a job at a tech company when his would-be employer posed an unusual request: Would he submit a handwriting sample?

Baffled, he asked why. It turned out the company had an analyst in Israel who regularly reviewed potential employees' handwriting. "It's a very effective way to find out what people's true personalities are and what they're like to work with," he recalls being told.

But for job candidates themselves requests like these pose a quandary: You're asked to do something in the hiring process that just seems weird, and makes you uncomfortable. If you express hesitation or flat-out refuse, you risk losing the job. Employers may label you uncooperative or overly sensitive. But if you suppress your discomfort and perform the task, you may be ignoring a red flag telling you this company isn't the place for you.

"Some of these odd things really are sort of shining a light on what some of the company quirks are, and maybe you need to make the decision that it's not a good fit," says Linda Dominguez, an executive coach based in Coarse Gold, Calif. Of course, "when you're unemployed, that's a really hard thing to do."

A few years ago, a client came to Ms. Dominguez after receiving an odd request. The woman was meeting with an internal recruiter at a real-estate company about a senior human-resources job. The recruiter asked the woman to have her photograph taken. When she asked why, she was told only that the hiring manager liked to see candidates before interviewing them.

She felt uncomfortable but obliged. Later, she wished she had declined because she didn't think the company should have needed to know what she looked like before landing an interview with the hiring manager, Ms. Dominguez says. She wasn't offered the job, but ended up at a different company with a better job title, higher pay, and a culture she felt was a better fit.

Simply expressing reluctance to comply with a request can hurt your chances of landing a job, career counselors say. Dan Squires, a career coach in Fort Lauderdale, Fla., recalls an acquaintance who was interviewing for a senior executive position at a company in the entertainment industry. He was asked to take a psychological test. He was so taken aback that he said no. A few hours later, after asking Mr. Squires for advice, he called the company to say he would take the test after all. But by then, Mr. Squires fears, the damage may have already been done. When people refuse to do things, Mr. Squires says, employers may think, "What else are we going to ask him to do and he'll say, 'uh-uh, not me?' " He didn't get the job, and Mr. Squires suspects it was at least partly because he initially balked about taking the test.

It's hard to tell whether an odd request is indicative of a broader problem at the company, or just a meaningless quirk of its hiring process. That's why it's so important to research the company by talking with as many people as possible inside and outside the firm. "You should have some sense [whether] this is an anomaly or something they do because they think it's warm and wonderful," says Dave Opton, chief executive of ExecuNet, a career management and recruitment network for executives and recruiters, based in Norwalk, Conn.

Mr. Archer felt uncomfortable when asked to take the handwriting test. "It really made me think about what was going on with this company because I actually started to have doubts about whether I wanted to work there," he says.

"It made me wonder what other processes this company had that would be kind of 19th century," he says.