Whether you are arrested for allegedly possessing a drug such as heroin or cocaine, a weapon including a gravity knife or firearm, or some marijuana, the contraband the police claim you possessed may not have been on your person. That is, you are being charged with PL 220.03 (drug possession), PL 265.01 (weapon possession) or PL 221.10 (marijuana possession), but the police did not see or recover the contraband from your hand, pocket, body, etc. The law is clear in these circumstances. Assuming the allegations in the complaint against you are sufficient (the elements must be proven beyond a reasonable doubt if and when there is a trial), prosecutors can push forward in a case regardless if your possession was considered actual or constructive.
Although you will have a much further in depth consultation with your own New York criminal lawyer who will explain the different types of possession to you, the difference between actual possession and constructive possession is fairly obvious. One is on your person and the other in an area where you have dominion and control. In other situations, even though your possession was not physical, if the contraband is in plain view or in a car, a legal presumption of your knowledge and possession may be attributed to your case.