Nearly 5,400 undocumented Connecticut residents made appointments to take a written driving test from the Department of Motor Vehicles Monday as the state began the first phase of its “Drive Only” license program.

The law, which was approved by the legislature last year and signed by the governor, allows undocumented immigrants to acquire drivers licenses. The goal is to get more of the state’s motorists registered and insured.

“It’s going to bring more vehicles into compliance that are being driven out there,” DMV spokesman Bill Seymour said Tuesday. “It has an effect on folks who have an accident or a crash and find that the vehicle involved wasn’t insured. It helps keeps everybody safe on the roads.”

Monday marked the beginning of the first stage of the program, when people were permitted to make an appointment online to take a written test when the DMV begins administering them next month.

Judging by the first day, interest in the program is enormous. Seymour said 5,387 people made appointments online and about 33,000 people visited the department’s webpage on the program.

“That’s huge. We never get anything near that on any given day for anything,” he said of the department’s website page views. “That tells us there’s a lot of people looking at this information.”

Seymour said it is difficult for the DMV to predict how many people are eligible to apply for the drive only licenses. The Pew Research Center estimated there were about 130,000 undocumented immigrants living in Connecticut as of 2012.

Despite the high demand for the new program, the DMV does not expect a spike in wait times for its normal customers. The agency has hired new staff members and capped the number of driving tests it will administer for the new licenses at 700 per week.

It has also been periodically closing DMV branches this week on a staggered basis to conduct employee training on the program. The agency’s Hamden office was closed Tuesday between 7:45 a.m. and 1 p.m. and a Waterbury branch will be closed during the same hours Wednesday. Offices in Willimantic and Norwalk will be closed later this week.

Lawmakers plan to hold an informational hearing on the program next Monday. In a press release, incoming House Minority Leader Themis Klarides questioned how the program will affect “the way the DMV does business and interacts with the public.” In a letter to DMV Commissioner Melody Currey, Klarides said it was important the public be aware of next week’s hearing.

“Regardless of whether people support the immigrant drivers’ licenses program, it is one of the most significant public safety initiatives ever adopted in this state. I believe it is important that a genuine effort be made to inform the public about the new law,” Klarides wrote.

Connecticut is not alone in adopting programs to permit undocumented residents to obtain drivers licenses. This year, Connecticut and California will join eight other states that have enacted similar policies, according to the National Immigration Law Center. The nearest state with an undocumented immigrant drivers license program is Vermont.

Seymour said Connecticut has tried to learn from the experiences of other states by reinforcing its computer system to handle the additional demand. He said the DMV is also seeking to avoid the high test failure rates experienced elsewhere.

“It’s paramount — it’s critical that those seeking a permit read that drivers manual,” he said.

Because of the agency’s cap on weekly tests, an applicant who fails the test may have to wait months before they get another appointment. Seymour encouraged people who are applying to take the test to read the ’ manual, which is also available in Spanish. He said they could also visit the department’s website at ct.gov/driveonly and download a practice test app.

Adults who pass the written test will receive a learners permit by mail, which they will have to hold for at least three months before taking a driving test. During that time, they will be required to take eight hours of driving classes. Prospective teen drivers face more stringent requirements.

Click here for a list of documents needed to sign up for the test.