Your standard TV set or monitor should not exceed about 0.2 mR/Hr of radiation from a distance of 5 cm from any part of the cabinet. Most TV monitor equipment is less than half of this amount.
The CRT has a coating on the inner wall of its glass envelope, and also there is a metal shadow mask or aperture grill in the front. There is also a metal shroud around its parameter.
The type of emission from the CRT is known as soft X-Ray emission. This is because it is low power, and is in the lower X-Ray region.
The X-Ray emission is strongest at the rear of the TV set because there is some opened area where the electron gun is located. But, this is very weak as well. The radiation from a TV or monitor is not being focused to one point, and is also below the threshold level of being dangerous.
The long term effect of the total radiation from normal operating TV equipment is not fully known. However, the effect of X-Ray radiation is accumulative over time if there are no breaks in between the exposures. As for standard focused X-Rays like the ones used in a medical or security facility, these and most of their effects are well known.
As for normal working TV equipment, when used normally, the total radiation is less that what you would get when walking on the street. There are many satellites beaming down signals, radio and TV broadcast stations, communications systems, and then cell phones.
The X-Ray radiation in a TV set is emitted from the effect of the High Voltage drive generating the electron beam. If the High Voltage exceeds the designed safety limit for the CRT, then there is concern that the X-Ray radiation may have some effect on anyone that is in close proximity to the CRT. The amount of by which the high voltage exceeds the design specfifications will determine the total X-Ray emission. Since this emission is not focused into a fine area, its immediate danger is also greatly reduced.
All TV sets by law must have in their design some type of protection to shut the TV down if there is excessive High Voltage, excessive High Voltage current drive, and a number of other safety criterias.
There is also the concern about electromagnetic radiation. In fact all radio frequencies are based on electromagnetic radiation (EMR).
There was a great concern about the low frequency EMR. This would come from the power supply, deflection amplifier stages, and then from the deflection yoke and flyback transformer. There different types of EMR from TV sets.
Concerning TV's and monitors, this radiation worry comes up from time to time. If a woman is pregnant it would be wiser for her to not expose the unborn baby by working close to a terminal or monitor. This nonexposure is a good policy to make sure that everyone is safe rather than suffer any type of damage or health risks.
As for a safety concern for a mother to be, or a small baby, they can be in front of a TV set but at least 5 to 7 feet away. From this distance there should not be any danger at all.
The above is from my personal observations and is very general. I have also read various publications over the years that pertain to this subject.
I have a personal concern about the radiation from TV sets and monitors because I do an extensive amount of service on these. I am also doing a lot of picture tube changes in monitor equipment. I am then exposed for a few hours because I must do the purity and convergence setups of these sets. I have some days where I work 10 to 12 hours doing TV and monitor service work.
If you want a TV monitor that will put out near zero X-Ray radiation, and very low electromagnetic radiation, then go for one of the new LCD flatscreen monitors.