This would really depend on whether you care or not of being detected in the process and how much you're willing to invest into equipment, but sure. Provided there aren't some other, obvious signs the camera is on, such as the pan and tilt motors working
Low-tech approach: This is actually really similar to how doctors test patients for involuntary reflex reaction with a light source directed in patients' eyes and observing dilation (or lack thereof) of their pupils.
Most well designed CCTV cameras would have what is called an Auto Iris (AI). Basically an automatic method of varying the size of a lens aperture, to allow the correct amount of light to fall on the imaging device. The lens would include a tiny motor and an amplifier, which are used to maintain a desired voltage video signal as produced by varying levels of light falling on its image sensor.
By changing the level of light this camera's AI sensor receives, you could visually inspect the camera's iris movement even from an angle it can not record you (depending on its depth of field), or even audibly inspect the presence of such AI motor. Since these would be precision step (or stepper) motors, you would hear either a distinct buzz of it rotating, or the faint click when it's adjusted its step. Beware though, some ultra silent stepper motors have been developed already, tho I have yet to see CCTV cameras actually using them.
Similar testing could be applied to other camera's components (e.g. auto-focus), with varying degree of how stealthy the tester could remain during this testing.
High-tech approach: This is easy and rather obvious - electronic bug detectors are capable of detecting compromising emanations (basically EMI:
RF -> microwave -> IR fields in their descending wavelength / increasing frequency). Obviously they would all have some way of telling you which direction the compromising emanations are originating from, and most also at what specific frequencies and their exact strength.
Such devices are getting fairly cheap nowadays, and you can buy pretty decently capable ones off local resellers for up to a few hundred dollars, or even a second-hand one for roughly a quarter of that price off online resellers. Since the choice is fairly good, I won't give you any links to specific products, not wanting to endorse any specific manufacturer.
This detection would work both for wired, as well as wireless CCTV cameras. Wired CCTV systems would produce what is called a ballanced signal when on, which is a video signal that has been converted to enable it to be transmitted along 'twisted pair' cables, while the wireless (RF, or less common IR that require direct line of sight from the camera to the receiver) CCTV systems are even more apparent and would transmit higher energy radiation in their specified range (on top of compromising emanations from its internal circuitry).
Now, the other part of your question - detecting, if the video/audio feed is actually being recorded - is a bit more tricky to answer and would greatly depend on what system we're talking of here:
Analogue recording systems (rare nowadays) would actually add a bit more latency to the EM field emanating closed-loop when switched on (producing feedback spike in sine wave oscillation), basically moving the signal termination point a bit further on the power line (or separate signal cable, if not combined). This might, or might not be detectable by your equipment. Mind you, I do mean here only the exact moment when the recording device is switched on or off, and you would have a lot harder time detecting which state it's on, if it's in continuous mode of operation. Knowing the system beforehand and actually measuring its signal levels when on/off would obviously help.
Digital CCTV systems are a fair bit trickier to detect, if they're actually recording or not. In fact, you wouldn't be able to tell the difference between merely a receiver being on, or the recording system also doing its job that's connected to the receiver. With a bit of luck, you'd be dealing with direct-controllable IP cameras that would have a variable bit-rate (VBR) A/V feed encoder chip. This change in required bit-rate can be detected by better electronic bug detectors, but knowing the change in detectable EMI for the exact CCTV system beforehand would be of great help. With CBR/ABR (constant or average bit-rate) encoders, you'd most probably be out of luck though.
Now, I didn't write anything about disabling them, since you're not really inquiring about that, but maybe just a quick note that it's actually getting easier the more advanced they get, and with most new ones all you need is a decent pocket/torch size green laser (532 nm) directed for a few seconds directly into their CCD/CMOS sensor. The higher their resolution, the faster they will give up, depending also on laser's Watt rating, how much light diffraction are we talking of due to lens elements arrangement, their focal point, e.t.c. On wireless systems, you could actually detect their sensor's death by observing a sudden drop in compromising emanations intensity (camera's onboard video compression would be at its best with all the images of some framerate being the same, thus lowering the wireless frequency transmissions, i.e. lowering bandwidth).
Just mind, that CCTV cameras might be a whole lot more than cameras only, and pack audible and/or activity (movement / proximity / pressure change / presence of other compromising emanations / ...) detection sensors as well. And the most funny of all (to me, as I wouldn't really care of being detected or not) is being highly equipped for any eventuality, but then unwittingly manage to disturb some wildlife (bats, birds, rodents,...) with your presence, that would fright and trigger the CCTV system's response for you.