I can't speak for Carlsbad specifically but as a general rule...
No you cannot touch any bats in any cave!
Unless you are a genuine biologist studying the animals in a serious project. Nor should you disturb them by, e.g. shining your lamp directly at them.
In the UK unauthorised, deliberate handling of any bat anywhere without appropriate permission is illegal, but like wilfully collecting stalactites, it is regarded as wrong anyway throughout the caving world.
The Playboy Club Rule applies: Look, Don't Touch
People want to see the cave and the bats. Carlsbad Caverns is one of the largest caves in the whole world!
Carlsbad Caverns is located in New Mexico.
Carlsbad Caverns in New Mexico got its name from the nearby town of Carlsbad. The caverns were formally named in 1923 by the US government, taking inspiration from the famous Luray Caverns in Virginia.
US Congress changed the designation and the name of Carlsbad Cave National Monument, created in 1923, to Carlsbad Caverns National Park in 1930. Carlsbad Cavern, without the "s", is the name of the main tour cave. There are 117 caves known in the park.
Carlsbad Caverns is located in the state of New Mexico.
Two colonies of bats roost within Carlsbad Cavern. The larger population is estimated at about 400,000 bats, the other about 300-400.
Carlsbad caverns
Carlsbad Caverns is located in New Mexico.
Carlsbad Caverns is part of the Chihuahuan Desert.
Carlsbad Caverns may be found near the city of Carlsbad in New Mexico.
Carlsbad Caverns are located in the Guadalupe Mountains of southeastern New Mexico.
Open entrances. They were used in prehistoric times.