Can the police or tow companies impound a vehicle from private property in California?

They may not unless strict requirements by law are met. Laws regarding authority to cause the towing and storage of a vehicle differ among the states. Generally speaking, and I'm paraphrasing, a person, agency, or company must have and be able to show authority and reason to tow a vehicle from anywhere in order to legally do so.

The authority of police or tow companies to tow and store a vehicle must come from a Judge, the vehicle owner, or property owner unless it is stolen, blocking the entrance or exit to public parking, or is located within 15 feet of a fire hydrant. Briefly, officers of the CHP, local police, and sheriff departments receive due authority from the state, city, or county agencies respectively to operate within the territorial boundaries owned or controlled by the respective government authorities; however, jurisdiction may overlap in accordance with intergovernmental agency contracts. This authority does extend to or include off highway property, such as property belonging to a business or private citizen. Private property is any property not owned or leased by the state, city or county government. Authority to tow from private property must come from the vehicle or private property owner in the form of a written request or from a judge signed warrant to seize stated vehicle. A state vehicle or civil code number does not represent authority.

Without the vehicle owner's permission, a towing company may not tow from private property without written authorization from the private property owner or lessee and with that person present at the time of the tow to verify the reason for the tow. See CVC-22658(l)(1)(A) Any tow company that tows a vehicle without such authorization or fails to present a photocopy of this authorization to the vehicle owner at the time of paying for towing and storage fees (CVC-22658(l)(1)(C)) is liable to the vehicle owner for 4 times the towing and storage fees charged. See CVC-22658(l)(4)&(5). The same is true if the tow company fails to obviously post their top fee rates or that they accept payments with a credit card (CVC-22658(k)(2)) where payments are received, or if they charge an excessive amount. See CVC-22658(j)(2)

Applicable vehicle codes must comply with other vehicles codes that are stated to apply to other vehicle codes, such as is stated in CVC-22658(p), to be legally enforced except when the enforced vehicle code states otherwise. For example, CVC-22651 or the codes it lists under 22651(p) do not stand alone and are legally enforceable only when in compliance with other codes such as CVC-22658.

Related codes include but are not limited to the following:

California Vehicle Code Sections:
14602.6
22650
22651
22653
22658 This code is in addition to and applies to all other vehicle codes.
22658(l) Very Important
22658(p) Very Important
22851.3
22953
22852.5

California Civil Code Sections
3070 & 3074

Use the search engine in www.findlaw.com for additional state codes.